Consider two streams of cash flows, A and B. Stream A’s first cash flow is $8,900 and is received three years from today. Future cash flows in Stream A grow by 4 percent in perpetuity. Stream B’s first cash flow is –$10,000, is received two years from today, and will continue in perpetuity. Assume that the appropriate discount rate is 12 percent.
What is the present value of each stream?
Answer:
| Prasent Value |
|
| Stream A | 88,687.82 |
| Stream B | 74,404.76 |
Working Notes for the above answer is as under
In this sum we need to apply the perpetuity formula to find the PV of stream A. This formula values the stream as of one year before the first payment and therefore this growing perpetuity formula values the stream of cash flow as of year 2
Next step is to discount the PV at the end of the year 2 back 2 year to find the PV on today
PV (A) =( C3 / (R-g) ) / (1+R)2
PV(A) = ( 8900 / (0.12-0.04)) / ( 1+0.12)2
Solving this equation we will get,
PV(A)= $ 88,687.82
Foe fing PV of Stream B we need apply the perpetuity formula to find the PV of stream B. This formula discount the stream back to 1 year
Next step is to discount the PV at the end of the year 1 back 1 year to find the PV on today
PV (B) =( C2 / R) / (1+R)
PV(B)= ( 10,000 /0.12) / (1.12)
Solving this equation we will get,
PV(B)= $ 74404.76
