Question

2. The formula for the present value of payment Y between any two periods j and k is

a. Compute the present value of a stream of $75,000 payments over 40 years at an interest rate of 5%

b. Compute the present value of a stream of $75,000 payments from years 1 through 20, followed by a stream of $100,000 payments from years 21 through 40, both at an interest rate of 5%.

c. How much higher is the present value in (c) versus (b)? Are you surprised it isn’t even higher?

Answer 1

Ans A)

We would use interest rate tables for calculation

Annuity=$75000

r=5%

T=40

Present value of streams can be calculated as

PV= A(P/A,r,T)

Go to interest rate tables then table belongs to 5% and then Column headed with P/A and row 40

PV =75000(P/A,5%,40)=75000*17.159=1,286,925

Ans B)

Using the same methodology

PV=75000(P/A,5%,20)+100000(P/A,5%,20)/(1.05)^20=75000*12.463+100000*12.462*0.3769=1,404,455.47

Ans C)

Difference between PV of part a) & part b) is

1,404,455.47-1,286,925=117,530

As higher payments of $100000 starts very late i.e after 20 years and discount factors beyond 20 years has lesser weightage hence the new PV is not much higher than it seems to be due to higher payoffs in future stream of cashflows