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Chapter 13 Homework Soltions
13.2 (a) Doubleday: Te = 9.2 + (1-0.092)(34) = 40.07% TI (in millions) = 2.8 + 0.9 โ 1.4 โ 0.85 = $1.
Merritt-Douglas: Te = 7.5 + (1-0.075)(34) = 38.95% TI (in millions) = 4.7 + 0.25 โ 3.1 โ 0.97 = $0.
(b) Use the average federal tax rate of 34%, not the total effective rate Te.
Doubleday: Federal tax estimate = 1,450,000(0.34) = $493, Merritt-Douglas: Federal tax estimate = 880,000(0.34) = $299,
(c) Doubleday: Taxes = 113,900 + 0.34(1,450,000 โ 335,000) = $493, Percent of revenue = 493,000/3.7 million = 13.3%
Merritt-Douglas: Taxes = 113,900 + 0.34(880,000 โ 335,000) = $299, Percent of revenue = 299,200/4.95 million = 6.0%
Doubleday M-D Te 40.07% 38.95% TI $1,450,000 $880, Tax estimate $493,000 $299, Tax (table) $493,000 $299, % revenue 13.3% 6.0%
13.3 (a) Te = 9.8 + (1 โ 0.098)(31%) = 37.76% TI = 4.9 โ 2.1 โ 1.4 = $1.4 million Tax estimate = 1.4 million(0.3776) = $528,
(b) 528,640/4.9 million = 10.8%
13.4 (a) TI = 320,000 โ 149,000 โ 95,000 = $76,
(b) Use Table 13- Taxes = 13,750 + 0.34(76,000-75,000) = $14,
(c) T (^) e = 10.5 + (1 โ 0.105)(18.5 = 27.06% Tax estimate = 76,000(0.2706) = $20, Percent of GI = 20,566/320, = 6.43%
13.9 Estimate before-tax MARR by Equation [13.9]. Tabulate CFBT; calculate AW.
Before-tax MARR = 10%/(1-0.35) = 15.4%. (All $ values are in $1000 units.)
Year GI E P and S CFBT 0 $-1900 $- 1 $800 $-100 700 2 950 -150 800 3 600 -200 400 4 300 -250 700 750
PW = -1900 + 700(P/F,15.4%,1) + โฆ + 750(P/F,15.4%,4)
AW = -9(A/P,15.4%,4) = -9(0.3531)
Equipment is (marginally) not justified using CFBT values.
13.10 Determine MACRS depreciation, taxes and CFAT. Assume negative tax will increase CFAT and AW.(All $ values are in $1000 units.)
TI = GI โ E - Depr CFAT = CFBT - taxes
Year GI E P and S CFBT Depr TI Taxes CFAT 0 $-1900 $-1900 $- 1 $800 $-100 700 $633 $ 67 $23 677 2 950 -150 800 845 -45 -16 816 3 600 -200 400 281 119 42 358 4 300 -250 700 750 141 -91 -32 782
13.11 Determine AW of CFAT at 10%.
AW = -1900 + 677(P/F,10%,1) + โฆ + 782(P/F,10%,4) = [-1900 + 677(0.9091) + 816(0.8264) + 358(0.7513)
- 782(0.6830)](0.31547) = 192(0.31547) = $
Equipment is justified using CFAT values.
13.28 Find after-tax PW of costs over 4-year study period. DR is involved on the defender trade.
Defender SL depreciation is (45,000-5000)/8 = $
Annual tax = (-E โ Depr)(Te) = (-7000 โ 5000)(0.35) = $-4200 (savings)
CFAT = CFBT โ taxes = -7000 โ (-4200) = $-
PWD = -35,000 + 5000(P/F,12%,4) โ 2800(P/A,12%,4) = -35,000 + 5000(0.6355) โ 2800(3.0373) = $-40,
Challenger MACRS depreciation over n = 5, but only 4 years apply
Defender trade depreciation recapture must be included. Defender BV 3 = 45,000 โ 3(5000) = $30, SP = $35, DR = SP โ BV = 5, Tax on DR = 5,000(0.35) = $
Challenger first cost = -24,000 - 1750 = $-25, MACRS depreciation is based on $24,000 first cost
Year Exp P and S Rate Depr TI Taxes CFAT 0 -25,750 -25, 1 -8000 0.3333 8,000 -16,000 -5,600 -2, 2 -8000 0.4445 10,668 -18,668 -6,534 -1, 3 -8000 0.1481 3,554 -11,554 -4,044 -3, 4 -8000 0 0.0741 1,778 -9,778 -3,422 -4,
PWC = -25,750 โ 2400(P/F,12%,1) - โฆ - 4578(P/F,12%,4)
Select the challenger with a lower PW of cost. Spreadsheet solution follows
13.31 (a) Amanda: debt Charlotte: equity
(b) Find FW at end of year.
Amanda: i = 18/12 = 1.5% per month FW = 2000(F/P,1.5%,12) = 2000(1.1956) = $2391.
Charlotte: effective i = 8% per year FW = 2000(F/P,8%,1) = 2000(1.08) = $
13.32 (a) Equity (b) Debt (c) Equity (d) Debt (e) Equity
