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ipn [44]
3 years ago
9

A rich donor gives a hospital $100,000 one year from today. Each year after that, the hospital will receive a payment 5% larger

than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 9%?
A) $772,173.49
B) $585,987.27
C) $467,922.22
D) $779,843.27
Business
1 answer:
wariber [46]3 years ago
5 0

Answer:

D) $779,843.27

Explanation:

The present value of this donation = Donation in Year 1/(1+ discount rate)^9 + Donation in Year 2/(1+ discount rate)^8 + ….. + Donation in Year 2/(1+ discount rate)^1

= $100,000/(1+9%) + $100,000*(1+5%)/(1+9%)^2 +$100,000*(1+5%)^2/(1+9%)^3…. +$100,000*(1+5%)^9/(1+9%)^10 = $779,843.27

Or we can easily input in excel and generate NPV as file attached; in which the formula is NPV(discount rate, cash inflow year 1 : cash inflow year 10) = (9%, 100000,100000*(1+5%)….,100000*(1+5%)^9) = $779,843.27

Download xlsx
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Explanation:

Investment A

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Value of Investment A = 1500 000/r

Investment B

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Value of investment B = (1200 000 x (1+0.03))/(r - 0.03)

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1236000(r) = 1500000(r - 0.03)

(r - 0.03) = 1236000( r)/1500000

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r = 0.03/0.176 = 0.170454545

R = 17.045%

The cost of capital that will make both investments to be equal is 17.045%

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