Question

Given a discount rate of 5.6 percent per year, what is the value at year 0 of a perpetual stream of $4,000 annual payments (cash inflows) that begins at year 0 and grows at a rate of 3 percent for all subsequent years?

a) $66,666.67
b) $71,428.57
c) $75,000.00
d) $80,000.00

Answer 1

The value at year 0 of a perpetual stream of $4,000 annual payments with a discount rate of 5.6% is $71,428.57. Hence, b) is correct.

Step-by-step explanation:

To calculate the present value of a perpetual stream of payments, we can use the formula:

PV = C / r

Where PV is the present value, C is the cash inflow per period, and r is the discount rate per period.

In this case, the cash inflow per period is $4,000 and the discount rate is 5.6%. To calculate the present value at year 0, we plug in these values into the formula:

PV = $4,000 / 0.056 = $71,428.57

Therefore, the value at year 0 of the perpetual stream of $4,000 annual payments is $71,428.57.