BUS 106.Solution to Homework A.Spring 2016 (3)

# BUS 106.Solution to Homework A.Spring 2016 (3) - BUS 106...

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BUS 106 –Spring Qtr.2016 Professor Y. Peter Chung Solutions to Homework A Chap 8 13 . a.   NPV for each of the two projects, at various discount rates, is tabulated below. NPV A  = –\$20,000 + [\$8,000   annuity factor ( r %, 3 years)] = –\$20,000 +  3 ) (1 1 1 000 , 8 \$ r r r NPV B  =  3 ) 1 ( 000 , 25 \$ 000 , 20 \$ r Discount Rate NPVA NPVB   0% \$4,000 \$5,000   2% 3,071 3,558   4% 2,201 2,225   6% 1,384 990   8% 617 –154 10% –105 –1,217 12% –785 –2,205 14% –1,427 –3,126 16% –2,033 –3,984 18% –2,606 –4,784 20% –3,148 –5,532 1

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From the NPV profile, it can be seen that Project A is preferred over Project B if the discount rate is above 4%.  At 4% and below, Project B has the higher NPV. b. IRR A  = discount rate ( r ), which is the solution to the following equation: 000 , 20 \$ ) (1 1 1 \$8,000 3 r r r r  = IRR A  = 9.70% IRR B  = discount rate ( r ), which is the solution to the following equation: 3 ) 1 ( 000 , 25 \$ 000 , 20 \$ r  = 0  IRR B  = 7.72% Using a financial calculator, find IRR A  = 9.70% as follows: Enter PV =  (–)20; PMT = 8; FV = 0;  n  = 3; compute  i. Find IRR B  = 7.72% as follows: Enter PV = (–)20; PMT = 0; FV = 25;  n  =  3; compute  i. 34. a. Present value = Cash flow at end of year \$5,000 \$100,000 Discount rate – growth rate 0.10 0.05 NPV = –\$80,000 + \$100,000 = \$20,000 b. Recall that the IRR is the discount rate that makes NPV equal to zero: (– Investment) + (PV of cash flows discounted at IRR) = 0 0 05 . 0 IRR 000 , 5 \$ 000 , 80 \$ Solving, we find that: IRR = (\$5,000/\$80,000) + 0.05 = 0.1125 = 11.25% Chap11 6. a. 2
b. The average risk premium was 4.67%. c. The variance (the average squared deviation from the mean) was 5.48%.  Therefore, standard deviation =  % 41 . 23 0548 . 14. a.  Interest rates tend to fall at the outset of a recession and rise during boom  periods.   Because bond prices move inversely with interest rates, bonds provide  higher returns during recessions when interest rates fall. b. r stock  = [0.2   ( .05)] + (0.6   .15) + (0.2   .25) = .13 or 13.0% r bonds  = (0.2   .14) + (0.6   .08) + (0.2   .04) = .084 or 8.4% Variance (stocks) = [0.2   ( .05   .13) 2 ] + [0.6   (.15   .13) 2 ] + [0.2   (.25 – .13) 2 ] = .0096 Standard deviation = 9.80% or .098 0096 . Variance (bonds) = [0.2   (.14   .084) 2 ] + [0.6   (.08   .084) 2 ] + [0.2    (.04   .084) 2 ] = .001024 Standard deviation =  % 20 . 3 001024 . c. Stocks have both higher expected return and higher volatility.  More risk- averse investors will choose bonds, while those who are less risk-averse  might choose stocks.

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