Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

24 pv 121676 70 pmt 1000 fv if the ytm rises from 10

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Unformatted text preview: t of the last withdrawal, we can increase the real dollar withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal. So, the last withdrawal in nominal terms will be: FV = PV(1 + r)t FV = $6,657.74(1 + .04)(30 + 25) FV = $57,565.30 28. In this problem, we need to calculate the future value of the annual savings after the five years of operations. The savings are the revenues minus the costs, or: Savings = Revenue – Costs Since the annual fee and the number of members are increasing, we need to calculate the effective growth rate for revenues, which is: Effective growth rate = (1 + .06)(1 + .03) – 1 Effective growth rate = .0918 or 9.18% The revenue for the current year is the number of members times the annual fee, or: Current revenue = 500($500) Current revenue = $250,000 The revenue will grow at 9.18 percent, and the costs will grow at 2 percent, so the savings each year for the next five years will be: Year 1 2 3 4 5 Revenue 272,950.00 298,006.81 325,363.84 355,232.24 387,842.55 Costs 76,500.00 78,030.00 79,590.60 81,182.41 82,806.06 Savings 196,450.00 219,976.81 245,773.24 274,049.82 305,036.49 $ $ $ Now we can find the value of each year’s savings using the future value of a lump sum equation, so: FV = PV(1 + r)t 229 Year 1 $196,450.00(1 + .09)4 = 2 $219,976.81(1 + .09)3 = 3 $245,773.24(1 + .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 = $97,523.83 230 Calculator Solutions 1. a. Enter 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 20 N 50 N 2.5% I/Y 50 N 4.5% I/Y 20 N 7.5% I/Y 20 N 5% I/Y 20 N 2.5% I/Y PV $610.27 PMT $1,000 FV PV $376.89 PMT $1,000 FV PV $235.41 PMT $1,000 FV 50 N 3.5% I/Y PV $1,000.00 $35 PMT $1,000 FV PV $802.38 $35 PMT $1,000 FV PV $1,283.62 ±$1,050 PV $35 PMT $1,000 FV Solve for 3.547% × 2 = 7.09% 4. Enter 27 N I/Y 3.547% $39 PMT $1,000 FV 3.8% I/Y ±$1,175 PV Solve for $48.48 × 2 = $96.96 $96.96 / $1,000 = 9.70% PMT $48.48 $1,000 FV 231 5. Enter Solve for 6. Enter Solve for 13. P0 Enter 15 N 7.60% I/Y PV €1,070.18 ±¥87,000 PV €84 PMT €1,000 FV 21 N I/Y 6.56% ¥5,400 PMT ¥100,000 FV Miller Corporation 26 N 3.5% I/Y PV $1,168.90 $45 PMT $1,000 FV Solve for P1 Enter Solve for P3 Enter Solve for P8 Enter Solve for P12 Enter Solve for Modigliani Company P0 Enter Solve for P1 Enter Solve for 24 N 4.5% I/Y 26 N 4.5% I/Y 2 N 3.5% I/Y 10 N 3.5% I/Y 20 N 3.5% I/Y 24 N 3.5% I/Y PV $1,160.58 $45 PMT $1,000 FV PV $1,142.12 $45 PMT $1,000 FV PV $1,083.17 $45 PMT $1,000 FV PV $1,019.00 $45 PMT $1,000 FV PV $848.53 $35 PMT $1,000 FV PV $855.05 $35 PMT $1,000 FV 232 P3 Enter Solve for P8 Enter Solve for P12 Enter Solve for 20 N 4.5% I/Y PV $869.92 $35 PMT $1,000 FV 10 N 4.5% I/Y PV $920.87 $35 PMT $1,000 FV 2 N 4.5% I/Y PV $981.72 $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 PV Solve for $964.54 ∆ PLaurel% = ($964.54 – 1,000) / $1,000 = –3.55% PHardy Enter 30 N 5% I/Y PV Solve for $846.28 ∆ PHardy% = ($846.28 – 1,000) / $1,000 = –15.37% If the YTM suddenly falls to 6 percent: PLaurel Enter 4 3% N I/Y PV Solve for $1,037.17 ∆ PLaurel % = ($1,037.17 – 1,000) / $1,000 = + 3.72% PHardy Enter 30 N 3% I/Y $40 PMT $1,000 FV $40 PMT $1,000 FV PV Solve for $1,196.00 ∆ PHardy % = ($1,196.00 – 1,000) / $1,000 = + 19.60% $40 PMT $1,000 FV All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in interest rates. 233 15. Initially, at a YTM of 10 percent, the prices of the two bonds are: PFaulk Enter Solve for PGonas Enter Solve for 16 N 5% I/Y 16 N 5% I/Y $30 PMT $1,000 FV PV $783.24 PV $1,216.76 $70 PMT $1,000 FV 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 $30 PMT $1,000 FV PV Solve for $1,101.06 ∆ PGonas% = ($1,101.06 – 1,216.76) / $1,216.76 = –9.51% If the YTM declines from 10 percent to 8 percent: PFaulk Enter 16 4% N I/Y PV Solve for $883.48 ∆ PFaulk% = ($883.48 – 783.24) / $783.24 = +12.80% PGonas Enter 16 N 4% I/Y $70 PMT $1,000 FV $30 PMT $1,000 FV PV Solve for $1,349.57 ∆ PGonas% = ($1,349.57 – 1,216.76) / $1,216.76 = +10.92% $70 PMT $1,000 FV 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 ±$960 PV $37 PMT $1,000 FV I/Y Solve for 4.016% YTM = 4.016% × 2 = 8.03% 234 17. The company should set the coupon rate on its new...
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