Question

1. Simes Innovations, Inc., is negotiating to purchase exclusive rights to manufacture and market a solar-powered toy car. The car’s inventor has offered Simesthe choice of either a one-time payment of $1,500,000 today or a series of 5 year-end payments of $385,000.

a. If Simes has a cost of capital of 9%, which form of payment should the company choose? b. What yearly payment would make the two offers identical in value at a cost of capital of 9%?

c. Would your answer to part a of this problem be different if the yearly payments were made at the beginning of each year? Show what difference, if any, that change in timing would make to the present value calculation.

d. The after-tax cash inflows associated with this purchase are projected to amount to $250,000 per year for 15 years. Will this factor change the firm’s decision about how to fund the initial investment?

2. Rieger International is attempting to evaluate the feasibility of investing $95,000 in a piece of equipment that has a 5-year life. The firm has estimated the cash inflows associated with the proposal as shown in the following table. The firm has a 12% cost of capital.

Year (t) ​​​​Cash inflows (CFt)

1 $20,000

2 25,000

3 30,000

4 35,000

5 40,000

a. Calculate the payback period for the proposed investment.

b. Calculate the net present value (NPV) for the proposed investment.

3. Pound Industries is attempting to select the best of three mutually exclusive projects. The initial investment and after-tax cash inflows associated with these projects are shown in the following table.

Cash flows ​​​Project A​​ Project B ​​Project C

Initial investment (CF0)​​ $60,000​​$100,000​​ $110,000

Cash inflows (CFt),t1 to 5 ​$20,000​​ $ 31,500​​ $ 32,50

a. Calculate the payback period for each project.

b. Calculate the net present value (NPV) of each project, assuming that the firm has a cost of capital equal to 13%.

Answer 1

Question - 1

Given information,

Simes Innovations Inc, has two options to make payment i) One time payment of $ 1,500,000 ii) Annual payments of

$ 385,000

Part - a

We have to decide what form of payment to be opted by company if the Cost of Capital is 9% per annum. To make the decision we need the Present values for both the options and the option with lower present value to be opted because it results in a saving of cost to the company.

Present value of option - 1 is given in the question itself = $ 1,500,000

Present value of option - 2 = ??

Formula to be used C x [ (1 – (1+i)^-n) / i ] where C is the cash flow per period, i is the cost of capital and n is the frequency of payments.

By using the above value we get Present value of option -2 as $ 1,497,515.74.

Therefore, the present value of option - 2 is less than option -1. Hence it is advisable to opt for periodic payments.

Part - B

Here we need to find the Periodic payment at which the Present values under both of the options will be equal.

Formula to be used PV= C x [ (1 – (1+i)^-n) / i ] where PV is the present value

By substituting the values in above formula we get

$ 1,500,000 = C x [(1-(1+0.09)^-5)/0.09]

By solving the above equation we get the value of C as $ 385,638.69

Hence the periodic payment should be $ 385,368.69

Part - C

We have to calculate the present value of Option - 2 if the yearly payments were made at the begining of each year i.e., payment made at the begining of 2nd year is equivalent ot payment made at end of 1st year and so on.

By using the above formula we can calculate the present values of payments made at the begining of 2,3,4,5 years and the payment made at begining of 1st year should be added to the resulting present value.

Present value = $ 1,632,292.15

Therefore , it is advisable to prefer Opt -1.

Part-d

It is given that if after tax cash inflows projected from the Purchase amounts to $ 250,000 per year for 15 years. Since the decision is to make a choice among two purchase options provided by the Seller we need to consider only the Cash outflows associated in two options and make a decision. And the cash inflows are same under both the options so it does not make a difference with respect to decision making. Alternativley if the cash inflows differ in each of the option then it will impact the decision making.

Question - 2  

Part - a

Year	Cash Inflow	Cumulative Cash inflow	Cash Outflow
0	-95000		-95000
1	20000	20000
2	25000	45000
3	30000	75000
4	35000	110000
5	40000	150000

Payback period of investment will be in 4th year

PBP = years before full recovery + (Unrecovered cost at start of year)/ cash flow during the year

PBP = 3 + 20000/35000

PBP = 3.57 years approximatedly or 3 years 6 months 25 days.

Part - B

we have to calculate the NPV of the project

NPV = Present value of cash inflow - Present value of cash outflow

NPV = 104081 - 95000

NPV = $ 9081

Question - 3

Part - a

Payback period

Particulars	Project-A	Project-B	Project-C
Initial Investment	60000	100000	110000
Cash inflows per annum	20000	31500	32500
Payback period	3 years	3.17 years	3.38 years

Formula used for Payback period = Initial investment / Cash inflows per annum

Part-B

Given cost of capital = 13%

n= 5 years

NPV = Present value of cashinflows - present value of cash outflows

For project A, NPV = $ 70344.63 - $ 60000 = $ 10344.63

For project B, NPV = $ 110792.78 - $ 100000 = $ 10792.78

For project C, NPV = $ 114310 - $ 110000 = $ 4310

There fore best project to invest is Project - B since NPV is more.