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The following are exercises in present values:a. $100 at the end of three years is worth how much today, assuming a discount rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent?b. What is the aggregate present value of $500 received at the end of each of the next three years, assuming a discount rate of (i) 4 percent? (ii) 25 percent?c. $100 is received at the end of one year, $500 at the end of two years, and $1,000 at the end of three years. What is the aggregate present value of these receipts, assuming a discount rate of (i) 4 percent? (ii) 25 percent?d. $1,000 is to be received at the end of one year, $500 at the end of two years, and $100 at the end of three years. What is the aggregate present value of these receipts assuming a discount rate of (i) 4 percent? (ii) 25 percent?e. Compare your solutions in Part (c) with those in Part (d) and explain the reason for the differences.
Part a (i) PV of $100 when discount rate is 100% = $100 / (1 +100%) ^3 = $12.5 (ii) PV of $100 when discount rate is 10% = $100 / (1 +10%) ^3 = $75.13 (iii) PV of $100 when discount rate is 0% = $100 / (1 +0%) ^3 = $100 Part b (i) PV of $500 received at the end of each of the next three years at discount rate of 4% = $500 * PVIFA at 4% for 3 years = $500 * (1-1/1.04^3) / 0.04 = $1,387.55 (ii) PV of $500 received at the end of each of the next three years at discount rate of 25% = $500 * PVIFA at 25% for 3 years = $500 * (1-1/1.25^3) / 0.25 = $976.00 Part c (i) PV of receipts at discount rate of 4% = $100/1.04 + $500/1.04^2 + $1,000/1.04^3 = $1,447.43 (ii) PV of receipts at…

iscount rate of 25% = $100/1.25 + $500/1.25^2 + $1,000/1.25^3 = $912.00 Part d (i) PV of receipts at discount rate of 4% = $1000/1.04 + $500/1.04^2 + $1,00/1.04^3 = $1,512.72 (ii) PV of receipts at discount rate of 25% = $1000/1.25 + $500/1.25^2 + $1,00/1.25^3 = $1,171.20 Part e Value in D is more than C because majority of cash flows in case of D are received in earlier years than in case of C and hence the effect of discounting is less in case of D.

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