Question

Someone has offered to buy you a financial instrument that has the following cash flows: - You will not receive any cash for the first 7 years. The first time you will receive a cash low will be at the year 10 end of year 8. You will receive $100 at the end of year 8, $200 at the end of year 9, and $300 at the end of - You will receive another payment of $200 at the end of year 11, and the payment will remain the same forever. - You will need to pay a service fee. The service fee is as follows: you will pay $100 each year from year1 to year 5 (i.e. you will make 5 payments in total. The first payment will occur at the end of year 1, and the last payment will occur at the end of year 5) Suppose that the discount rate is 10%. How much this financial instrument is worth to you? * You have to show your work to get credit. Format B I U

Answer 1

Let the cash flow for Year x be CFx

inflows are designated as +ve and outflows as -ve

Hence, CF1 = -100
CF2 = -100
CF3 = -100
CF4 = -100
CF5 = -100
CF6 =
CF7 =
CF8 = 100
CF9 = 200
CF10 = 300
CF11 = 200
........... perpetuity of $200

interest rate = r = 0.10

Now, we need to find the NPV

NPV = CF0/(1+r) + CF1/(1+r)² +.......

=> NPV = -100/1.1 - 100/1.1² - 100/1.1³ - 100/1.1⁴ - 100/1.1⁵ + 0 + 0 + 100/1.1⁸ + 200/1.1⁹ + 300/1.1¹⁰ +  (200/0.10)/1.1¹¹

In the last step we have calculated the value of the perpetuity = P/r = 200/0.10

=> NPV = $569.04

Hence, the financial instrument is worth $569