Problems: P 9.1-9.4, 9.8 & 9.11

HM 707 Health Management Foundations II

Problem 9.1

Find the following values for a lump sum assuming annual compounding: a) The future value of $500 invested at 8 percent for one year:

FVN = FV1= PV × (1 +I)N = $500 x (1 + 0.08) = $500 x 1.08 = $540 b) The future value of $500 invested at 8 percent for five years:

FVN = FV5= PV × (1 +I)N = $500 x (1 + 0.08)5 = $500 x (1.08)5 = $734.66

c) The present value of $500 to be received in one year when the opportunity cost rate is 8 percent (discounting):

PV = FVN = $5001 = $500 = $462.96 (1 + I)N (1 + 0.08)1 (1.08)1

d) The present value of $500 to be received in

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PV = $2,457.84

b) The future value of $400 per year for 10 years at 10 percent-

Future Value= (Interest rate, Number of periods, Payment) formula in excel

PV = 0, PMT = -400, N = 10, I = 10, FV =?

FV = $6,374.97

c) The present value of $200 per year for 5 years at 5 percent

PV (Annuity) = (Interest rate, number of periods, Payment) formula in excel

I= 5%, N=5, PMT=$-200, PV=?

PV = $865.90

d) The future value of $200 per year for 5 years at 5 percent-

Future Value= (Interest rate, Number of periods, Payment) formula in excel

PV = 0, PMT = -200, N = 5, I = 5, FV =?

FV = $1,105.13

Problem 9.8

What is the present value of perpetuity of $100 per year if the appropriate discount rate is 7 percent? Suppose that interest rates doubled in the economy and the appropriate discount rate is now 14 percent. What would happen to the present value of the perpetuity?

PV (Perpetuity) = Payment = PMT Interest Rate I

PV = $100 = $1,428.57 0.07

PV (Perpetuity) = Payment = PMT Interest Rate I

PV = $100 = $714.29 0.14

Therefore the perpetuity decreases because of the higher interest rate. This is because the value of the perpetuity changes dramatically when the opportunity costs (interest rates) change.

Problem 9.11

Consider the following investment cash flows:

Year Cash Flow 0