Question

Kiran is thinking about purchasing a birthday gift for his girlfriend. Instead of a handbag or jewellery, he will buy a financial asset for her. He thinks this is a wonderful gift because this asset will payout a certain annual cash flow from her 26^th birthday until her 35^th birthday. The cash flow will be $5,000 on her 26^th birthday and this will grow at a rate of 3% each year. How much would Kiran have to pay on his girlfriend's 25th birthday for this asset if he paid the fair value assuming a constant interest rate of 5% p.a. compounding annually?

Answer 1

P = First cash flow = $5,000

g = growth rate = 3%

r = annual interest rate = 5%

n = 10 years

Present Value = [P / (r-g)] * [1 - [(1+g)/(1+r)]^n]

= [$5,000 / (5%-3%)] * [1 - [(1+3%)/(1+5%)]^10]

= $250,000 * 0.174951923

= $43,737.9808

Therefore, amount needed to pay for the gift is $43,737.98