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Engineering Economy, 8th edition
Leland Blank and Anthony Tarquin
Chapter 10
Project Financing and Noneconomic Attributes
Working with MARR
10.1 The two primary sources of capital are debt and equity. Debt capital refers to capital
10.2 The project that is not undertaken due to lack of funds, say B, that has a ROR of i*B, in
10.3 (a) Higher risk - raise
(f) Government imposition of price controls – lower
10.4 12 - 8 = 4% per year
10.7 (a) Bonds are debt financing
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PW measure: Select projects A, E, C and D to total $29 million. Opportunity cost is
12.8%, the ROR of project B
10.9 (a) MARR = WACC + required return = 8% + 4% = 12%. The 3% risk factor is
D-E Mix and WACC
10.10 (a) Calculate the two WACC values.
(b) Let x1 and x2 be the maximum costs of debt capital
10.11 Debt portion of $15 million represents 40% of the total
10.12 Debt: 16 + 30 = $46 million
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D-E mix is 74%-26%
10.13 WACC = cost of debt capital + cost of equity capital
10.14 Compute the WACC for each D-E mix. For example, the 70-30 D-E mix results in
0-100 12.50
D-E mix of 50%-50% has the lowest WACC value.
10.15 Solve for X, the cost of debt capital
10.16 Company’s equity = 30(0.35) = $10.5 million
10.17 (a) Business: all debt; D-E = 100%-0%
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Engineer: FW = 25,000 + 25,000(F/P,7%,1)
= 25,000 + 26,750
= $51,750
Two checks: $25,000 to parents and $26,750 to credit union
(c) Business: 4%
10.18 First Engineering: D-E mix = 87/(175-87) = 87/88
10.19 Total financing = 3 + 4 + 6 = $13 million
10.20 Before-taxes:
After-tax approximation: Insert Equation [10.4] into the before-tax WACC relation.
10.21 (a) Determine the after-tax cost of debt capital, Equation [10.4], and WACC
(b) After-tax WACC = 0.25(14.5%) + 0.75(6.4%)
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14.0 million(0.08425) = $1,179,500
As more and more capital is borrowed, the company risks higher loan rates and
owns less and less of itself. Debt capital (loans) becomes more expensive and
harder to acquire.
Cost of Debt Capital
10.22 (a) Before-tax cost of debt capital is 8%
(b) Interest = 4,000,000(0.08)
(c) Approximation using Equation [10.4] is
10.23 (a) 0 = 2,800,000 – 196,000(P/A,i*,10) – 2,800,000(P/F,i*,10)
(b) NCF is determined using Equation [10.6]
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i* = 4.69% (RATE function)
After-tax cost of debt capital is 4.69% per year
10.24 Before-tax bond annual interest = 6 million*0.06 = $360,000
estimate the after-tax debt cost of 6%(1 - 0.4) = 3.60% from Equation [10.4]).
10.25 (a) 0 = 19,000,000 – 1,200,000(P/A,i*,15) – 20,000,000(P/F,i*,15)
(b) Tax savings = 1,200,000(0.29) = $348,000
10.26 (a) Bank loan
Annual loan payment = 800,000(A/P,8%,8)
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0 = 800,000(A/P,i*,8) - 123,525
(A/P,i*,8) = 0.15441
i* = 4.95% (RATE function)
Bond issue
Annual bond dividend = 800,000(0.06) = $48,000
Bond financing is cheaper.
10.27 (a) Face value = $2,500,000 = $2,577,320
0.97
Factor solution:
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$27.17 > 0; i* < 0.75%
By interpolation,
Spreadsheet solution:
Cost of Equity Capital
10.30 (a) Re = 1.90/80 + 0.03
10.31 Let x = dividend growth rate
10.32 Re = 0.035 + 0.92(0.05)
10.34 (a) Dividend method: Re = DV1/P + g
(b) CAPM: (The return values are in percent)
= 5.51%
(c) Set dividend method Re = 0.0551 and solve for DV1
For any initial dividend less than 75.4¢ per share, the CAPM estimate will be larger.
10.35 Last year CAPM computation: Re = 4.0 + 1.10(5.1 – 4.0)
Equity costs slightly more this year in part because the company’s stock became more
10.36 Total equity and debt fund is $15 million.
Equity WACC = (retained earnings fraction)(cost) + (stock fraction)(cost)
Different D-E Mixes
10.37 A large D-E mix over time is not healthy financially because this indicates that the
10.38 (a) Find cost of equity capital using CAPM.
Find i* on 50% equity investment.
(b) Determine WACC and set MARR = WACC. For 50% debt financing at 8%,
10.39 100% equity financing
MARR = 8.5% is known. Determine PW at the MARR.
60%-40% D-E financing
Cost of 60% debt capital is 9% for the loan.
Annual NCF = project NCF - loan payment
Calculate PW at the MARR on the basis of the committed equity capital.
Recommendation: Do not invest using either D-E plan, 0%-100% or 60%-40%
10.40 Determine i* for each plan
Plan 1: 80% equity means $480,000 funds are invested. Use a PW-based relation.
Plan 2: 50% equity means $300,000 invested.
Plan 3: 40% equity means $240,000 invested.
Determine the MARR values.
MARR3 = WACC3 = 0.4(7.5%) + 0.6(10%) = 9.0%
(c ) MARR1 = (8.00 + 7.5)/2 = 7.75%
Make the decisions using i* values for each plan. The ‘?’poses the question “Is the plan
justified in that i* ≥ MARR?”. The decision is no (N) or yes (Y) for each plan.
Part (a) Part (b) Part (c)
Plan i* MARR ?+ MARR ?+ MARR ?+
10.41 (a) Calculate the two WACC values for financing alternatives 1 and 2
(b) Let x1 and x2 be the maximum costs of debt capital for each plan, respectively
10.42 MARR = WACC + 12.5%. Total equity and debt fund is $15 million. Debt capital
