Question

1) Albert has an investment worth 275,042 dollars. The investment will make a special payment of X dollars to Albert in 7 month(s) and the investment also will make regular, fixed monthly payments of 2,390 dollars to Albert forever. The expected return for the investment is 0.92 percent per month and the first regular, fixed monthly payment of 2,390 dollars will be made to Albert in 1 month. What is X, the amount of the special payment that will be made to Albert in 7 month(s)?

2) An investment is expected to generate annual cash flows forever. The first annual cash flow is expected in 1 year and all subsequent annual cash flows are expected to grow at a constant rate annually. We know that the cash flow expected in 3 year(s) from today is expected to be 1,600 dollars and the cash flow expected in 8 years from today is expected to be 3,320 dollars. What is the cash flow expected to be in 5 years from today?

3) An investment, which has an expected return of 13.2 percent, is expected to make annual cash flows forever. The first annual cash flow is expected in 1 year and all subsequent annual cash flows are expected to grow at a constant rate of 2.28 percent per year. The cash flow in 1 year from today is expected to be 33,260 dollars. What is the present value (as of today) of the cash flow that is expected to be made in 4 years?

4) Indigo River Banking just bought a new race track. To pay for the race track, the company took out a loan that requires Indigo River Banking to pay the bank a special payment of 19,710 dollars in 7 month(s) and also pay the bank regular payments.   The first regular payment is expected to be 4,860 dollars in 1 month and all subsequent regular payments are expected to increase by 0.31 percent per month forever. The interest rate on the loan is 1.9 percent per month. What was the price of the race track?

5) You own a store that is expected to make annual cash flows forever. The cost of capital for the store is 10.72 percent. The next annual cash flow is expected in one year from today and all subsequent cash flows are expected to grow annually by 1.27 percent. What is the value of the store if you know that the cash flow in 7 years from today is expected to be 13,100?

6) Goran has an investment worth 75,779 dollars. The investment will make a special payment of X to Goran in 5 quarters in addition to making regular quarterly payments to Goran forever. The first regular quarterly payment to Goran is expected to be 2,000 dollars and will be made in 3 months. All subsequent regular quarterly payments are expected to increase by 0.42 percent per quarter forever. The expected return for the investment is 3.6 percent per quarter. What is X, the amount of the special payment that will be made to Goran in 5 quarters?

Answer 1

Solution 1:

We would be using Future Value formula to find the value of Investment @ end of 7 months

In the question Present Value = 275042; Monthly Rate = 0.92%; Nper = 7 months

Future Value = Present Value* (1+monthly rate)^nper = 275042*(1+0.92%)^7 = 293251.14

Difference between Future Value & Present Value will give us the incremental value i.e. =293251.14 - 275042= 18209.14

By Dividing the Incremental Value by 7 we will get Monthly Incremental Value = 18209.14/7 = 2601.31

If we deduct monthly payment of 2390 by 2601.31 we would get = 211.31

Then, multiplying 211.31 by 7 we would get 1479.14 and this 1479.14 is our X i.e. Special Payment

Solution 2:

Year 3 Annual Cash Flow expected to be 1600, Year 8 Annual Cash Flow expected to be 3320

We would use RATE formula from the excel i.e. =RATE (nper,,PV,[FV],0)

Where nper =5years (Year 8 - Year 3); PV = 1600 expected cash flow in Year 3 and FV = 3320 expected cash flow in Year 8

By inputting the aforesaid values in the formula we would get RATE = (5,,1600,-3320,0) = 15.72%

We would use this Rate of 15.72% to compute the value of Investment today by using Present Value formula

Present Value = Future Value /(1+rate)^nper; Where Future Value = 1600 expected cash flow at Year 3, rate = 15.72% and nper = 3years

PV= 1600 / (1+15.72%)^3 = 1032.55 this is the Investment value today.

Now to find expected Cash flow at Year 5 we would use Future Value formula i.e. FV= PV*(1+rate)^nper

Here Present Value = 1032.55; Rate = 15.72%; Nper=5; FV= 1032.55*(1+15.72%)^5 = 2142.53

Thus Cash Flow expected to be in 5 years from now = 2142.53

Sol 3:

Expected Cash flow in Year 1 = 33260, thereafter each annual cash flow grows at a constant rate of 2.28% per year

So Expected Cash Flow in Year 2 should be = 33260*(1.0228) = 34018.33; Expected Cash Flow in Year 3: 34018.33*(1.0228) = 34793.95

and Expected Cash Flow in Year 4 should be = 34793.95*(1.0228) = 35587.25

We would now use the Present Value formula to find the present value of the Cash flow received in Year 4 from today

Present Value = Future Value / (1+rate)^nper; Here Future Value = 35587.25 and Rate = 13.2% and nper = 4years

Thus Present Value = 35587.25 / (1+13.20%)^4 = 21672.48

Present Value of Cash flow that is expected to be made in Year 4 = 21672.48

Solution 4:

WE would first calculate how much Indigo River banking is paying the Bank in 7 months

For that we know that Indigo has to pay Bank a special payment of 19,710 dollars

We also know that First Regular payment is expected to be 4860 in Month 1 then increasing at the Rate of 0.31% per month

To know the Future Value after 7 months of Regular Payments We have used Future Value Annuity formula i.e.

Future Value of Annuity = Annuity * [(1+r)^n - 1 / r]

Here Annuity = 4860; Rate = 0.31% and nper = 7 months thus FVA= 4860*[(1+0.31%)^7 - 1 /0.31%]

This will result to 34338.03 it is nothing but the sum total of the regular payments till 7 months

If we add these regular payments till 7 months to the Special Payment i.e. =19710+ 34338.03 = 54048.03

This will give us the Future Value of the Loan or Price paid to buy the Race Track at month 7

To find the price of the Race Track we would use Present Value formula

Present Value = Future Value / (1+rate)^nper

Here Future Value = 54048.03; rate =1.9% per month and nper = 7 months

Present Value = 54048.03 / (1+1.9%)^7 = 47376.24

Thus 47376.24 is the price of the Race Track