Question

Suppose you have the option to extend a loan to a friend this year for $1000 in exchange for repayment next year of $1100 (the $1100 is the principal plus interest). Every year, however, the friend has the option to borrow $1000 again in exchange for $1100 repayment one year later, i.e. the friend can roll over the debt. You know this friend well and know that he will always roll over the debt and will never default.

a. Assume neither of you will ever die. What is the NPV of this infinite stream of loans if you have a discount rate of 8%?

b. Now assume your friend today is t=0 and your friend will die immediately after paying back his loan at t=60. What is the NPV of this finite stream of loans if you have a discount rate of 8%?

Answer 1

4)

a)

at t = 0 cash outflow will be 1000

at t = 1 to t = infinite cash inflow 1100 and outflow 1000 so net cash inflow = 100 (1100 - 1000)

NPV = Present value of future cash flows - initial cash outflow

Given discount rate = 8%

Present value of perpetuity = cash flow / discount rate

= 100 / 8% = 1250

so NPV = 1250 - 1000 = 250

b)

here cash flows will be as follows

at t = 0 cash outflow = 1000

from t = 0 to t = 59 cash inflows 100 (calculated as above)

at t = 60 cash inflow = 1100

so Present value of future cash flows = 100*PVIFA(r = 8% ; n = 60) + 1000*PVF(r = 8% ; n = 60)

= 100*12.37655 + 1000*0.009876

  = $1247.53

NPV = 1247.53 - 1000 = $247.53 (rounded to two decimals)