P9-18 Personal finance problem: Weighted-average cost of capital (LG 6; Intermediate)
John’s weighted average cost of student loans is given by:
Column →1 2 3 = 2 $ 4 = 1
Rate Balance Weight Weighted Cost
Loan 1
6.00%
$20,000
31.25%
1.88%
John should not consolidate his loans because the bank’s offer of 7.2% exceeds the current cost.
P9-19 Calculation of individual costs and WACC (LG 3, LG 4, LG 5, and LG 6; Challenge)
a. Cost of debt: Net proceeds = Par value ($1,000) – Discount ($30) – Flotation costs ($30) =
$940. The before-tax cost of debt is the interest rate that makes the following equation hold:
Bn = + + … + +
[Note: Net proceeds from sale (third term in parentheses) must be entered as a negative
number.]
The after-tax cost of debt is rd (1 – T ), where T is the tax rate. If that rate is 40%, after-tax cost
b. Cost of preferred stock: The cost of new preferred stock (rp) is given by (Dp Np), where Dp is
c. Cost of retained earnings: The price of Lang common stock (P0) is $90, dividend growth has
been 6% per year and is expected to continue, and the next expected dividend is $7. When a
d. Cost of new common stock: The cost of new common stock (rn) is given by (D1 Nn) – g, where
Nn is net sales proceeds. Flotation costs are $5 per share, and new shares must be underpriced
e. Type of Capital Weights (%) Cost Weighted Cost
With retained earnings
Long-term
debt 0.30 5.18% 1.555%
Preferred
Type of Capital Weights (%) Cost Weighted Cost
With new
common
stock
Long-term
debt 0.30 5.18% 1.555%
Preferred
*problem asks for rWACC to the nearest 0.1%
common stock.
P9-20 Weighted-average cost of capital (LG 6; Intermediate)
a. The weighted average cost of capital, rWACC [wd rd (1 – T)] + [wp rp]+ [ws rs], where
respectively. American has no preferred stock, so rWACC = (0.50 0.06) (0.50 0.12) 9.0%.
b. With more leverage, American’s rWACC (0.70 0.06) (0.30 0.12) 0.042 0.036 7.8%.
c. Greater leverage exposes shareholders to more risk. Bond holders have a prior claim to
American’s operating income, so more debt means more interest expense to cover before the
e. More leverage means a greater risk of missing scheduled dividend payments and even declaring
cost of capital may not decline with greater reliance on low-cost debt.
P9-21 Ethics problem (LG 1; Intermediate)
GE’s long string of good earnings reports made the company seem less risky, thereby reducing
returns required by the firm’s bond and stockholders and the firm’s cost of capital. If investors learn
GE is really more risky than it appeared in the past, required returns and the cost of capital will rise.
Case: “Making Star Products’ Financing/Investment Decision”
Case studies are available on www.pearson.com/mylab/finance.
This case requires students to (1) calculate the costs of long-term debt, preferred stock, and common stock
equity, (2) determine the points where the cost of each funding source jumps, and (3) distill this information
into a weighted average cost of capital for use in assessing projects.
a. Cost of debt: The before-tax cost of debt (rd) is the interest rate that makes the following equation hold:
Bn = + + … + +
where:
In Excel, rd may be found with the RATE command; proper syntax is: =rate(15,90,-960,1000).
The after-tax cost is rd (1 – T ), where T is the firm’s tax rate. For the first $450,000 in bond sales
Cost of preferred stock: rp = Dp Np, where Dp is the constant preferred dividend and Np is the net
Cost of common stock equity: The cost of retained earnings (rr) is the required return on common
stock: (D1 P0) + g, where D1 is the next expected dividend, P0 the stock price, and g expected dividend
b. Weighted average cost of capital (rWACC) for Star Products, with a 40% tax rate:
Type of Capital Weights Cost of Capital
1. Long-term debt ≤ $450,000 and
common equity less ≤ $1,500,000:
Long-term debt 0.30 5.71%
3. Long-term debt > $450,000 and
common equity > $1,500,000:
c. (1) Star wants to raise funds in proportion to its current capital structure. To find the
borrowing threshold where the weighted average cost of capital (rWACC) rises, recognize 30 cents
(2) To find the retained-earnings threshold where rWACC rises, recognize 60 cents of every dollar
raised should be common equity, and $1.5 million in retained earnings is available. So rWACC will
(3) There is no need to look at the case where Star borrows less than $450,000 and uses more than
d. Ranking investment projects from highest to lowest rate of return:
The following diagram depicts project ranking (jagged Investment Opportunity Schedule or IOS line)
and the weighted average cost of capital (jagged WACC line) with a 40% tax rate. The IOS line plots
The following diagram depicts the same project ranking (jagged IOS line ), but this time with the
e. Star Products should undertake all projects with rates of return exceeding the cost of capital. These
projects have positive net present value and will, therefore, enhance the value of the firm. Based on the
in cheap equity (retained earnings). With a 21% tax rate, Star will still accept all five projects.
(1) If Star can sell only $450,000 in debt, its total funding constraint is $1.5 million ($450,000. 0.30).
Given this constraint, the firm will accept projects starting with the highest return (C) and moving
(2) If Star can use no more than $750,000 in common equity, its total funding constraint is $1.25
million ($750,000 0.60). Such a constraint means Star will undertake only Projects C and D
(4) A long-term debt cap of $1.0 million implies a total funding constraint of $3,333,333.33 million
these projects collectively required $2.4 million.
Spreadsheet Exercise
Answers to Chapter 9’s Nova Corporation exercise on measuring the cost of capital are available on
www.pearson.com/mylab/finance.
Group Exercise
Group exercises are available on www.pearson.com/mylab/finance .
This chapter’s exercise focuses on measuring and applying the weighted average cost of capital (WACC).
Groups will conduct research on the financing mix used by their shadow firms and use that knowledge to
construct a balance sheet with a similar capital structure for their fictitious firms. Next, students will use this
Integrative Case 4: “Eco Plastics Company”
This case focuses on the cost of capital. For a hypothetical firm, students will calculate the cost of
individual sources of capital (long-term debt, preferred stock, and common stock) as well as the weighted
average cost of capital with the current capital structure and a more highly leveraged capital structure. In the
process, they will learn financing with debt can be a double-edged sword—it is cheap but can boost the cost
of common stock enough to raise the weighted average cost of capital.
a. Cost of debt: Net proceeds from bond sales = par value – discount – flotation costs = $1,000 – $45 –
dollars ($1,000)
C = Coupon payment each period (10.5%) N = periods to maturity
(20)
b. Cost of preferred stock: Eco’s cost of selling preferred stock (rp) is Dp Np, where Dp is the expected
perpetual preferred dividend and Np is net proceeds from selling preferred stock.
c. Cost of common stock: CAPM is used to determine the cost of selling new Eco Plastics common
0.04)] = 15.7%.
ws are the weights applied to the cost of debt, preferred stock, and common stock respectively, rad is the
after-tax cost of debt, rp is the cost of preferred stock, and rn is the cost of common stock. The weight
e. (1) If the weights on the components change from 30%/20%/50% to 50%/0%/50%, Eco
Plastics’ beta coefficient (β) rises from 1.3 to 1.5. As a result, the risk premium on common stock
(2) The new weighted average cost of capital with the more expensive common equity (given a 40%
(3) Eco Plastics should retain its current financial structure. Replacing preferred-stock financing with
debt financing increases risk to holders of common stock. The resulting rise in the required rate of
return on common stock more than offsets the advantage of using low-cost debt, thereby boosting
the weighted average cost of capital.