Proposed project:
Alchemy Mines is considering an investment in the rights to a platinum mine.
Initial investment
The owner of the mine will sell the rights to Alchemy Mines at a cost of $1,000,000
payable immediately. Purchase of the rights entitles Alchemy Mines to all mining rights
provided mining commences within one year and continues without interruption until the
entire deposit is recovered and the land restored in compliance with regulatory
requirements. If mining does not commence in one year, the title to the mine reverts to
the seller.
Expected operating variables
The firm has made the following assumptions regarding operating cash flows for the
mine:
Recoverable platinum: 100,000 ounces
Current market price of platinum: $889.60 per ounce
Expected price of platinum in one year: $904.00 per ounce
Expected fixed costs of mining and refining: $750,000
Expected variable costs of mining and refining: $873.50 per ounce
Cost to restore the land and remediate environmental damage: $525,000
No taxes are paid on profits from the project
If the firm mines the platinum, all cash in- and out-flows from mining and selling the
platinum and for remediation will occur in one year.
Additional Information:
The firm estimates additional economic variables as follows:
Risk free interest rate equals 2.5%
Expected market return: 11.50%
Beta for platinum mining and smelting: 0.662
Standard deviation of annual returns on platinum prices: 0.1995
1. Use net present value analysis to determine whether the firm should accept the
proposed Alchemy Mines project.
a. Determine the amount and timing of all expected cash flows for the proposed
project.
b. Determine the appropriate discount rate (using CAPM).
c. Calculate NPV.

d. Indicate whether Alchemy Mines should accept the project based on it NPV
and explain.
2. Use option pricing analysis to determine whether Alchemy Mines should accept
the proposed platinum mine project.
a. Determine whether the project cash flows have the characteristics of a put
option or a call option.
b. Find the implicit “strike price,” that is, the expected spot platinum price at
which the firm will elect to commence mining and processing rather than just
walk away from the project. (Remember that for an option, the option premium is
a sunk cost and does not affect the decision to exercise.)
c. Calculate the option value of the mine using the Black-Scholes options pricing
model.
Note: You can calculate the option value for a single ounce of platinum
using per ounce price and costs, then multiply that by the total amount of
platinum to get the total option value of the mine. Alternatively, you can
calculate the option value using the total price of platinum and the total
costs.
d. Compare the option value of the mine to the cost to acquire rights to the mine
to determine whether to accept the project.
e. Indicate whether Alchemy Mines should accept the project and explain.

​Beryl's Iced Tea currently rents a bottling machine for $ 52 comma 000 per​ year, including all maintenance expenses. It is considering purchasing a machine instead and is comparing two​ options: a. Purchase the machine it is currently renting for $ 165 comma 000. This machine will require $ 21 comma 000 per year in ongoing maintenance expenses. b. Purchase a​ new, more advanced machine for $ 265 comma 000. This machine will require $ 18 comma 000 per year in ongoing maintenance expenses and will lower bottling costs by $ 13 comma 000 per year.​ Also, $ 37 comma 000 will be spent up front to train the new operators of the machine. Suppose the appropriate discount rate is 7 % per year and the machine is purchased today. Maintenance and bottling costs are paid at the end of each​ year, as is the cost of the rental machine. Assume also that the machines will be depreciated via the​ straight-line method over seven years and that they have a​ 10-year life with a negligible salvage value. The marginal corporate tax rate is 40 %. Should​ Beryl's Iced Tea continue to​ rent, purchase its current​ machine, or purchase the advanced​ machine? To make this​ decision, calculate the NPV of the FCF associated with each alternative.

Kim Inc. must install a new air conditioning unit in its main plant. Kim must install one or the other of the units; otherwise, the highly profitable plant would have to shut down. Two units are available, HCC and LCC (for high and low capital costs, respectively). HCC has a high capital cost but relatively low operating costs, while LCC has a low capital cost but higher operating costs because it uses more electricity. The costs of the units are shown here. Kim's WACC is 6%.

1. Which unit would you recommend?
   1. Since we are examining costs, the unit chosen would be the one that had the lower NPV of costs. Since LCC's NPV of costs is lower than HCC's, LCC would be chosen.
   2. Since we are examining costs, the unit chosen would be the one that had the lower NPV of costs. Since HCC's NPV of costs is lower than LCC's, HCC would be chosen.
   3. Since all of the cash flows are negative, the IRR's will be negative and we do not accept any project that has a negative IRR.
   4. Since all of the cash flows are negative, the NPV's cannot be calculated and an alternative method must be employed.
   5. Since all of the cash flows are negative, the NPV's will be negative and we do not accept any project that has a negative NPV.
   ?
2. If Kim's controller wanted to know the IRRs of the two projects, what would you tell him?
   1. The IRR cannot be calculated because the cash flows are all one sign. A change of sign would be needed in order to calculate the IRR.
   2. The IRR cannot be calculated because the cash flows are in the form of an annuity.
   3. The IRR of each project will be positive at a lower WACC.
   4. There are multiple IRR's for each project.
   5. The IRR of each project is negative and therefore not useful for decision-making.
   
   ?
3. If the WACC rose to 12% would this affect your recommendation?
   1. When the WACC increases to 12%, the IRR for LCC is greater than the IRR for HCC, LCC would be chosen.
   2. When the WACC increases to 12%, the IRR for HCC is greater than the IRR for LCC, HCC would be chosen.
   3. Since all of the cash flows are negative, the NPV's will be negative and we do not accept any project that has a negative NPV.
   4. When the WACC increases to 12%, the NPV of costs are now lower for LCC than HCC.
   5. When the WACC increases to 12%, the NPV of costs are now lower for HCC than LCC.
   
   ?
   
   Explain your answer and the reason this result occurred.
   1. The reason is that when you discount at a higher rate you are making negative CFs higher thus improving the IRR.
   2. The reason is that when you discount at a higher rate you are making negative CFs higher thus improving the NPV.
   3. The reason is that when you discount at a higher rate you are making negative CFs higher and this lowers the NPV.
   4. The reason is that when you discount at a higher rate you are making negative CFs smaller and this lowers the NPV.
   5. The reason is that when you discount at a higher rate you are making negative CFs smaller thus improving the NPV.
   
   ?

 ​Fingen's 19​-year, ​$1000 par value bonds pay 15 percent interest annually. The market price of the bonds is ​$1110 and the​ market's required yield to maturity on a​ comparable-risk bond is 12 percent.

a.)Compute the​ bond's yield to maturity.

b.)Determine the value of the bond to​ you, given your required rate of return.

c.)Should you purchase the​ bond?

1. Project L costs $35,000, its expected cash inflows are $14,000 per year for 8 years, and its WACC is 9%. What is the project's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations.

2. Project L costs $71,242.75, its expected cash inflows are $14,000 per year for 11 years, and its WACC is 14%. What is the project's IRR? Round your answer to two decimal places.

3. Project L costs $40,000, its expected cash inflows are $15,000 per year for 8 years, and its WACC is 9%. What is the project's MIRR? Round your answer to two decimal places. Do not round your intermediate calculations.

4. Project L costs $50,000, its expected cash inflows are $9,000 per year for 11 years, and its WACC is 13%. What is the project's payback? Round your answer to two decimal places.

5. Project L costs $40,000, its expected cash inflows are $9,000 per year for 8 years, and its WACC is 11%. What is the project's discounted payback? Round your answer to two decimal places.

NPV

Your division is considering two projects with the following cash flows (in millions):

1. What are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
   Project A    $ _____ million
   Project B    $ _____  million

   What are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
   Project A    $ _____  million
   Project B    $ _____  million

   What are the projects' NPVs assuming the WACC is 15%? Round your answer to two decimal places. Do not round your intermediate calculations. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Negative value should be indicated by a minus sign.
   Project A    $  _____ million
   Project B    $ _____  million

2. What are the projects' IRRs assuming the WACC is 5%? Round your answer to two decimal places. Do not round your intermediate calculations.
   Project A _____  %
   Project B _____  %

   What are the projects' IRRs assuming the WACC is 10%? Round your answer to two decimal places. Do not round your intermediate calculations.
   Project A  _____ %
   Project B  _____ %

   What are the projects' IRRs assuming the WACC is 15%? Round your answer to two decimal places. Do not round your intermediate calculations.
   Project A  _____ %
   Project B _____  %

3. If the WACC was 5% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 3.86%.)  
   ?

   If the WACC was 10% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 3.86%.)  
   ?

   If the WACC was 15% and A and B were mutually exclusive, which project would you choose? (Hint: The crossover rate is 3.86%.)  
   ?

The Saleemi​ Corporation's ​$1000 bonds pay 5 percent interest annually and have 9 years until maturity. You can purchase the bond for ​$1135.

a.)What is the yield to maturity on this​ bond?

b.)Should you purchase the bond if the yield to maturity on a​ comparable-risk bond is 5 ​percent?

A firm with a 13% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows:

0 1 2 3 4 5

Project M -$24,000 $8,000 $8,000 $8,000 $8,000 $8,000

Project N -$72,000 $22,400 $22,400 $22,400 $22,400 $22,400

1. Calculate NPV for each project. Round your answers to the nearest cent. Do not round your intermediate calculations.
   Project M $ ______
   Project N    $______

   Calculate IRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M   ______   %
   Project N    ______  %

   Calculate MIRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M  ______    %
   Project N    ______  %

   Calculate payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M   ______   years
   Project N   ______   years

   Calculate discounted payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M   ______   years
   Project N   ______   years

2. Assuming the projects are independent, which one(s) would you recommen

3. If the projects are mutually exclusive, which would you recommend?

4. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
   

 The 7​-year ​$1000 par bonds of Vail Inc. pay 9 percent interest. The​ market's required yield to maturity on a​ comparable-risk bond is 12 percent. The current market price for the bond is $ 940.

a.)Determine the yield to maturity.

b.)What is the value of the bonds to you given the yield to maturity on a​ comparable-risk bond?

c.)Should you purchase the bond at the current market​ price?

You have been hired as a capital budgeting analyst by Advent Sports, a sporting goods firm that manufactures athletic shoes. The firm believes it can generate another $10 million per year over the next 10 years by investing $10 million in a new distribution system (which will be depreciated over the system's 10-year life to a salvage value of zero). The firm will also need an initial increase of $1 million in net working capital to take on this project. The company expects its variable costs associated with these sales to be 40% of revenues, and additional advertising costs are anticipated to be $1 million per year. The firm is in the 40% tax bracket and has a hurdle rate of 8%. What is the project's NPV expected to be?

Select one:

A. $12,277,470

B. $14,556,754

C. $15,876,943

D. $17,834,221

You manage a risky portfolio with expected rate of return of 12% and a standard deviation of 24%.  The T-bill rate is 3%.

1. Suppose that your client decides to invest in your portfolio a proportion, y, of the total investment budget so that the overall portfolio will have an expected rate of return of 8.40%.  
   1. What is the proportion y?
   2. What is the standard deviation of the rate of return on your client’s portfolio at this new level y?

Assume the total cost of a college education will be $375,000 when your infant child enters college in 17 years. How much you invest at the end of each month in order to accumulate the required $375,000 at the end of 17 years if your monthly investments earn an annual interest rate of 4 percent, compounded monthly?

Dyrdek Enterprises has equity with a market value of $10.7 million and the market value of debt is $3.50 million. The company is evaluating a new project that has more risk than the firm. As a result, the company will apply a risk adjustment factor of 1.5 percent. The new project will cost $2.18 million today and provide annual cash flows of $571,000 for the next 6 years. The company's cost of equity is 11.03 percent and the pretax cost of debt is 4.87 percent. The tax rate is 39 percent. What is the project's NPV?