6 In calculating a composite or external rate or return for a given cash flow se

Question

6 In calculating a composite or external rate or return for a given cash flow sequence, if the reinvestment interest rate is greater than the internal rate of return, the resulting rate of return will be: A)Lower than the internal rate of return B)Greater than the internal rate of return C) Greater than the reinvestment interest rate D) Equal to the difference between the internal rate of return and the reinvestment interest rate 7 If an investor buys stock for $30,000 and receives dividends of $3,000 per year for five years and then sells the stock for $40,000, the rate of return on the investment is nearest to: A) B) C) D) 6% 8% 10% 15% 8 A permanent scholarship fund is started through a donation of $100,000. If five scholarships of $5,000 each are awarded each year beginning ten years from now, the rate of return for the invested money is nearest to: A) B) C) D) 6% 10% 14% 20% 9 A magazine subscription costs $45 per year at the beginning of each year, or $115 now for a three-year subscription. If the subscriber elects to pay the $115 now, the rate of return on the investment will be nearest to: A) B) C) D) 10% 18% 25% 35% 10 If a person invests $100,000 now and receives $4,000 per quarter for 10 years, the nominal rate of return per year is nearest to: A) B) C) 2% 4% 10%

Explanation / Answer

6) Answer - Greater than the internal rate of return.

IRR compares returns to costs by by finding the interest rate that produces a zero NPV for the investment cash flow stream. So if the reinvestment interest rate is more than the IRR, then resultant return rate is greater than internal rate of return.

7) Answer - 15%

30000 = 3000(P/A, i, 5) + 40,000(P/F, i, 5)

Assume i = 12%: 30,000 compared to 3000(3.6048) + 40,000(0.5674)
Result: $30,000 < $33,510; i is too big

Assume i = 18%: 30,000 compared to 3000(3.1272) + 40,000(0.4371) = $26,866
Result $30,000 > $26,866, i is too small

So the i is nearest to 15%

8) Answer - 10%

100,000 = 5 (5,000) (P/F, i, 9)

Assume i = 10%: $100,000 compared to 250,000(0.4241)

Result: $100,000 < $106,025; i is too big

AssumeTry i = 12%: $100,000 compared to 208,333(0.3606)
Result: $100,000 > $75,125; i is too small

So i is approx 10.5%

9) Answer is 18%

115 = 45 + 45(P/A, i, 2)

70 = 45(P/A, i, 2)

(P/A, i, 2) = 1.555

So i = 18%

10) Answer - 10%

100,000 = 4000(P/A, i, 40)

(P/A, i, 40) = 25.000

Nominal rate quarter is between 2% and 3%, say about 2.5%
Nominal i per year = 2.5(4) = 10%

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