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you will recieve payments forever. even after death. the prize will pay you $100,000 immediately ,...

you will recieve payments forever. even after death. the prize will pay you $100,000 immediately , it will then make payments every other year- next payment end of year 2, and each paymeny will be 8% larger than the last woth no end. of market retirn on an investment is 11% annul rate, what is the value of the prize today?
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Answer #1

Let the Cash Flows for Period n be denoted by CFn

Interest Rate = r = 11%

Growth rate in payment = g = 8%

Payment in Year 0 = 100000

Payment in Year 2 = 100000(1+g) = 100000(1+0.08)

Payment in Year 4 = 100000(1+g)2 = 100000(1+0.08)2

....

NPV = CF0 + CF2/(1+r)2 + CF4/(1+r)4 + ......

= 100000 + 100000(1+0.08)/(1+0.11)2 + 100000(1+0.08)2/(1+0.11)4 + ....

For an infinite series, a, ar, ar2, ar3, .... sum = a/(1-r)

=> NPV = 100000/(1 - (1+0.08)/(1+0.11)2) = $810059.17

Hence, Value of Prize = $810059.17

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