092 4 274049821 091 5 total future value of savings

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09)2 = 4 $274,049.82(1 + .09)1 = 5 Total future value of savings = Future Value $277,305.21 284,876.35 292,003.18 298,714.31 305,036.49 $1,457,935.54 He will spend $500,000 on a luxury boat, so the value of his account will be: Value of account = $1,457,935.54 500,000 Value of account = $957,935.54 Now we can use the present value of an annuity equation to find the payment. Doing so, we find: PVA = C({1 [1/(1 + r)]t } / r ) $957,935.54 = C({1 [1/(1 + . 09)]25 } / .09) C = $97,523.83 221 Calculator Solutions 1. a. Enter 20 N 2.5% I/Y 20 N 5% I/Y 20 N 7.5% I/Y 50 N 3.5% I/Y 50 N 4.5% I/Y 50 N 2.5% I/Y Solve for b. Enter Solve for c. Enter Solve for 2. a. Enter Solve for b. Enter Solve for c. Enter Solve for 3. Enter Solve for 3.547% 4. Enter 20 N I/Y 3.547% PMT $1,000 FV PV $376.89 PMT $1,000 FV PV $235.41 PMT $1,000 FV $35 PMT $1,000 FV $35 PMT $1,000 FV $35 PMT $1,000 FV $39 PMT $1,000 FV PV $610.27 PV $1,000.00 PV $802.38 PV $1,283.62 $1,050 PV 2 = 7.09% 27 N 3.8% I/Y $1,175 PV Solve for $48.48 2 = $96.96 $96.96 / $1,000 = 9.70% 222 PMT $48.48 $1,000 FV 5. Enter 15 N 7.60% I/Y Solve for 6. Enter 21 N Solve for 13. P0 Enter I/Y 6.56% PV 1,070.18 87,000 PV 84 PMT 1,000 FV 5,400 PMT 100,000 FV $45 PMT $1,000 FV $45 PMT $1,000 FV $45 PMT $1,000 FV $45 PMT $1,000 FV $45 PMT $1,000 FV $35 PMT $1,000 FV $35 PMT $1,000 FV Miller Corporation 26 N 3.5% I/Y 24 N 3.5% I/Y 20 N 3.5% I/Y 10 N 3.5% I/Y 2 N 3.5% I/Y Solve for P1 Enter Solve for P3 Enter Solve for P8 Enter Solve for P12 Enter Solve for PV $1,168.90 PV $1,160.58 PV $1,142.12 PV $1,083.17 PV $1,019.00 Modigliani Company P0 Enter 26 N 4.5% I/Y 24 N 4.5% I/Y Solve for P1 Enter Solve for PV $848.53 PV $855.05 223 P3 Enter 20 N 4.5% I/Y 10 N 4.5% I/Y 2 N 4.5% I/Y Solve for P8 Enter Solve for P12 Enter Solve for PV $869.92 PV $920.87 PV $981.72 $35 PMT $1,000 FV $35 PMT $1,000 FV $35
PMT $1,000 FV 14. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 8 percent. If the YTM suddenly rises to 10 percent: PLaurel Enter 4 N 5% I/Y $40 PMT $1,000 FV 30 N 5% I/Y $40 PMT $1,000 FV PV Solve for $964.54 PLaurel% = ($964.54 1,000) / $1,000 = 3.55% PHardy Enter Solve for PV $846.28 PHardy% = ($846.28 1,000) / $1,000 = 15.37% If the YTM suddenly falls to 6 percent: PLaurel Enter 4 N 3% I/Y $40 PMT $1,000 FV 30 N 3% I/Y $40 PMT $1,000 FV PV Solve for $1,037.17 PLaurel % = ($1,037.17 1,000) / $1,000 = + 3.72% PHardy Enter PV Solve for $1,196.00 PHardy % = ($1,196.00 1,000) / $1,000 = + 19.60% All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates. 224 15. Initially, at a YTM of 10 percent, the prices of the two bonds are: PFaulk Enter 16 N 5% I/Y 16 N 5% I/Y Solve for PGonas Enter Solve for PV $783.24 PV $1,216.76 If the YTM rises from 10 percent to 12 percent: PFaulk Enter 16 6% N I/Y PV Solve for $696.82 PFaulk% = ($696.82 783.24) / $783.24 = 11.03% PGonas Enter 16 N 6% I/Y PV Solve for $1,101.06 PGonas% = ($1,101.06 1,216.76) / $1,216.76 = 9.51% $30 PMT $1,000 FV $70 PMT $1,000 FV $30 PMT $1,000 FV $70 PMT $1,000 FV If the YTM declines from 10 percent to 8 percent: PFaulk Enter 16 N 4% I/Y $30 PMT $1,000 FV 16 N 4% I/Y $70 PMT $1,000 FV PV Solve for $883.48 PFaulk% = ($883.48 783.24) / $783.24 = +12.80% PGonas Enter PV Solve for $1,349.57 PGonas% = ($1,349.57 1,216.76) / $1,216.76 = +10.92% All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates. 16. Enter 18 N Solve for YTM = 4.016% I/Y 4.016% 2 = 8.03% $960 PV 225 $37 PMT $1,000 FV 17. The company should set the coupon rate on its new bonds equal to the required return; the required return can be observed in the market by finding the YTM on outstanding bonds of the company. Enter Solve for 4.650% 40 N I/Y 4.650% $1,063 PV $50 PMT $1,000 FV $1,068.88 PV $90 PMT $1,000 FV $871.55 PV $41.25 PMT $1,000 FV $90 PMT $1,000 FV 2 = 9.30% 20. Current yield = .0842 = $90/P0 ; P0 = $1,068.88 Enter Solve for 8 years 21. Enter N 8.0004 20 N Solve for 5.171% 2 = 10.34% 23. Bond P P0 Enter 5 N Solve for P1 Enter 7.81% I/Y I/Y 5.171% 7% I/Y $90 PV PMT Solve for $1,067.74 Current yield = $90 / $1,082.00 = 8.32% Capital gains yield = ($1,067.74 1,082.00) / $1,082.00 = 1.32% Bond D P0 Enter 4 N 7% I/Y 5

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