Question

Paul makes $600 deposits UP FRONT each year for 5 years. If he can earn 6%, how much are the deposits worth today?

Steve is evaluating his investment in Ajax. He expects to receive $14 next period and estimates that the payments will grow at a constant rate of 3% forever. If he requires a 15% return, what is the value of his investment? Round answer to the nearest dollar.

Answer 1

Part A:

PV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the begining of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.
PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$               600.00
Int Rate	6.000%
Periods	5

PV of Annuity Due = [ Cash Flow + Cash Flow * [ 1 - [(1+r)^-(n-1)]] / r ]
= [ $ 600 + $ 600 * [ 1 - [(1+0.06)^-4] ] / 0.06 ]
= [ $ 600 + $ 600 * [ 1 - [(1.06)^-4] ] / 0.06 ]
= [ $ 600 + $ 600 * [ 1 - [0.7921] ] / 0.06 ]
= [ $ 600 + $ 600 * [0.2079] ] / 0.06 ]
= [ $ 600 + $ 2079.06 ]
= $ 2679.06
Value today is $ 2679.06

Part B:

Value = CF next period / [ Required Ret - Growth Rate ]

= $ 14 / [ 15% - 3% ]

= $ 14 / 12%

= $ 116.67