Question

An investment pays $15,000 every other year forever with the first payment one year from today.

a.	What is the value today if the discount rate is 8 percent compounded daily? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the value today if the first payment occurs four years from today? (Use 365 days a year. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

If the constant payments (cashflows) are received forever at equal intervals, it is called as Perpetuity.

The value of perpetuity is calculated as Terminal value, which is the present value of all the future forever cashflows.

The terminal value (or present value in general) is obtained 1 year prior to the first cashflow.

Terminal Value of perpetuity is given by, TV = C/r

where C is cashflow = 15000

r is the interest rate or required rate of return

(a) Here, interest rate = 8% p.a. compounded daily

But r = effective annual interest rate = (1+0.08/365)^365 - 1

so, r = 0.0833 or 8.33%

Therefore, Present Value = Terminal Value = 15000/0.0833

= 180072.03

(b) Here, interest rate = 8% p.a. compounded daily

or r = 8.33% (calculated above)

Terminal Value, TV = 180072.03

But first cashflow is received after year 4,

So, TV is calculated for year 3.

Present Value, PV = present value of TV

Present value for a single cashflow is calculated as, PV = C/(1+r)^t

where C is cashflow = 180072.03

r is interest rate = 8.33% (calculated above)

t is no. of periods = 3

So, PV = 180072.03/(1+0.0833)^3

= 141644.60