Question

Suppose you 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.

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%?

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

NPV = -initial inv+perpetual CF/interest rate

=-1000+100/0.08=250

part 2

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 100*((1-(1+ 8/100)^-60)/(8/100))

PV = 1237.66

NPV = -iinitial inv+PV of CF = -1000+1237.66 = 237.66