Financial ACCG253 Management
Tutorial 10 Chapter 12
Cost of Capital
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require
multiple steps. Due to space and readability constraints, when these intermediate steps are included
in this solutions manual, rounding may appear to have occurred. However, the final answer for each
problem is found without rounding during any step in the problem.
Basic
3.
We have the information available to calculate the cost of equity, using the CAPM and the
dividend growth model. Using the CAPM, we find:
RE = .045+ 0.90(.08) = .1170 or 11.70%
And using the dividend growth model, the cost of equity is
RE = [$2.60(1.05)/$48] + .05 = .1069 or 10.69%
Both estimates of the cost of equity seem reasonable. If we remember the historical return on the
all ordinaries index, the estimate from the CAPM model is about average, and the estimate from
the dividend growth model is about two percent lower than the historical average, so we cannot
definitively say one of the estimates is incorrect. Given this, we will use the average of the two,
so:
RE = (.1170 + .1069)/2 = .1119 or 11.19%
17. a.
b.
Projects Y and Z.
Using the CAPM to consider the projects, we need to calculate the expected return of the
project, given its level of risk. This expected return should then be compared to the
expected return of the project. If the return calculated using the CAPM is high er than the
project's expected return, we should reject the project; if not, we accept the project. After
considering risk via the CAPM:
E[W] = .05 + .70(.13 .05) = .1060 > .10, so reject W
E[X] = .05 + .90(.13 .05) = .1220 < .125, so accept X
E[Y] = .05 + 1.20(.13 .05) = .1460 > .14, so reject Y
E[Z] = .05 + 1.80(.13 .05) = .1940 < .21, so accept Z
c. If the firms overall cost of capital were used as a hurdle rate, then Project X would be
incorrectly rejected; Project Y would be incorr ectly accepted.
21. We will begin by finding the market value of each type of financing. We find:
MVD = 8,000($1,000)(1.04) = $8,320,000
MVE = 200,000($75) = $15,000,000
And the total market value of the firm is:
V = $8,320,000+ 15,000,000
V = $23,320,000
So, the market value weights of the companys financing is:
D/V = $8,320,000/$23,320,000 = 0.3568
E/V = $15,000,000/$23,320,000 = 0.6432
Now, we can find the cost of equity using the CAPM. The cost of equity is:
RE1 = 0.06 + 1.10(.13 .06)
RE1 = 0.1370 or 13.70%
We can also find the cost of equity, using the dividend discount model. The cost of equity with
the dividend discount model is:
RE2 = ($3.40/$75) + .07 = .1153
RE2 = 0.1153 or 11.53%
Both estimates for the cost of equity seem reasonable, so we will use the average of the two. The
cost of equity estimate is:
RE = (.1370 + .1153)/2
RE = 0.1262 or 12.62%
The cost of debt is the YTM of the bonds, so:
P0 = $1,040 = $45(PVIFAR%,50) + $1,000(PVIFR%,50)
YTM = 4.30% 2
YTM = 8.61%
And the aftertax cost of debt is:
RD = (1 0.30)(.0861)
RD = .0603 or 6.03%
Now, we have all of the components to calculate the WACC.
The WACC under a imputation system is:
WACC = 0.3568(.0603) + .6432(.1262)(1-0.30) = 10.11%
27. First, we need to find the project discount rate. The project discount rate is the companys cost of
capital plus a risk adjustment factor. The companys WACC is:
WACC = 0.40(.08) + .60(.14)
WACC = 0.1160 or 11.60%
Adjusting for risk, the project discount rate is:
Project discount rate = 0.1160 .03
Project + discount rate = 0.1460 or 14.60%
The company should only accept the project if the NPV is zero (hopefully greater than zero.) T he
cash flows are an annuity. The present value of the savings is:
PVA = $215,000(PVIFA14.60%,8)
PVA = $977,589.79
The project should only be undertaken if its cost is less than $977,589.79.
29. a. Using the dividend discount model, the cost of equity is:
RE = [(0.80)(1.06)/$72] + .06
RE = .0718 or 7.18%
b. Using the CAPM, the cost of equity is:
RE = .05 + 1.20(.1250 .05)
RE = .1400 or 14.00%
c. When using the dividend growth model or the CAPM, you must remember that both are
estimates for the cost of equity. Additionally, and perhaps more importantly, each method of
estimating the cost of equity depends upon different assumptions.
Challenge
31.
a.
The $6 million cost of the land 3 years ago is a sunk cost and irrelevant; the $6.4 million
appraised value of the land is an opportunity cost and is relevant. So, the total initial cash
flow is:
CF0 = $6,400,000 9,800,000 825,000
CF0 = $17,025,000
b.
To find the required return for the project, we need to adjust the companys WACC for the
level of risk in the project. We begin by calculating the market value of each type of
financing, so:
MVD = 25,000($1,000)(0.96) = $24,000,000
MVE = 400,000($89) = $35,600,000
MVP = 35,000($99) = $3,465,000
The total market value of the company is:
V = $24,000,000 + 35,600,000 + 3,465,000
V = $63,065,000
Next, we need to find the cost of funds. We have the information available to calculate the
cost of equity, using the CAPM, so:
RE = .0520 + 1.20(.08)
RE = .1480 or 14.80%
The cost of debt is the YTM of the companys outstanding bonds, so:
P0 = $960 = $32.50(PVIFAR%,40) + $1,000(PVIFR%,40)
R = .03435 or 3.435%
YTM = 3.435% 2
YTM = 6.87%
And the aftertax cost of debt is:
RD = (1 .30)(.0687)
RD = .04809 or 4.81%
The cost of preferred share is:
RP = $6.5/$99
RP = .0657 or 6.57%
So, the companys WACC is:
WACC = .0481($24,000/$63,065) + .0657($3,465/$63,035) + .1480($35,600/$63,065)
WACC = .1055 or 10.55%
The company wants to use the subjective approach to this project because it is located
overseas. The adjustment factor is 2 percent, so the required return on this project is:
Project required return = .1055 + .02
Project required return = .1255 or 12.55%
c.
The annual depreciation for the equipment will be:
$9,800,000/8 = $1,225,000
So, the book value of the equipment at the end of five years will be:
BV5 = $9,800,000 5($1,225,000)
BV5 = $3,675,000
So, the aftertax salvage value will be:
Aftertax salvage value = $1,250,000 + .30($3,675,000 1,250,000)
Aftertax salvage value = $1,977,500
d.
Using the tax shield approach, the OCF for this project is:
OCF = [(P v)Q FC](1 t) + tCD
OCF = [($10,000 9,300)(11,000) 2,100,000](1 .30) + .30($9,800,000/8)
OCF = $4,287,500
e.
We have calculated all cash flows of the project. We just need to make sure that in Year 5
we add back the aftertax salvage value, the recovery of the initial NWC, and the aftertax
value of the land in five years since it will be an opportunity cost. So, the cash flows for the
project are:
Year
0
Flow Cash
$17,025,000
1
2
3
4
5
4,287,500
4,287,500
4,287,500
4,287,500
14,090,000
Using the required return of 12.55 percent, the NPV of the project is:
NPV = $17,025,000 + $4,287,500 (PVIFA12.55%,4) + $14,090,000/1.12555
NPV = $3,652,494.05
And the IRR is:
NPV = 0 = $17,025,000 + 4,287,500 (PVIFAIRR%,4) + $14,090,000/(1 + IRR)5
IRR = 19.42%