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Unformatted text preview: CD :3 ; facrqATg 6’“ Tc) (Ma~(b) hooker @ The market value of Charter Cruise Company‘s equity is $15 million, and the market value of its risksfree debt is $5 million. if the required rate of return on the equity is
20% and that on the debt is 8%. calculate the company's cost of capital. (Assume no taxes.) ‘
{liven li '1 SlSm D 2 35m 9 V. 2 li +1) = 32011:. n, 2 20945. m 2 8%. l} t {it Using the WACC formula
fit/«t (iii’Vi in til)?“ 1* (l 11} 1*rn‘? (15r’2tl)*2tl"fh + (5520)*8% e 15% +3% 17‘”). ® The market value of XYZ Corporation's common stock is 40 million and the market value of the risk‘free debt is 60 million. The beta of the company's common stock is
0.8, and the expected market risk premium is 10%. If the treasury bill rate is 6%, What
is the fimri‘s cost of capital? (Assume no taxes.) (liven E : $4t'1m D I $60m 9 V‘ ; li +1) = $100111. 5;: = 0.8. (EM — Rf) K 10% RI?
m 6%") r, = 6% +0.8*10% i: 14%. Also given 'R = 0. Using the WACC fornnila rtht : (PE/Vt )fg. HINV‘ )a (I T( run) 1 (40;1(}0)*‘4Q/b + (50/100)*6% : 5.60/6 +16% 19.2%. O A ﬁrm has zero debt in its capital structure. Its overall cost of capital is 10%. The ﬁrm is considering a new capital structure with 60% debt. The interest rate on the debt
is 8%. Assuming there are no taxes, work out the ﬁrm’s cost of equity capital With the new capital structure. I r
We are given that rm = 10%. rt) = 8%. and that D/A = 60% 9 D/E : 60140 = 1.5. Using MM 11. I
n. = rm «immunity m) 2 10% +(l.5)*(10% 8%) = 10% + 1.92% 213%. XYZ Company is considering its ﬁrst and only project. This project calls for an investment of $24
million. Suppose the project is expected to generate sales of $30 million per year. Annual costs account for
75% of the sales. The annual sales. costs, and. therefore income. are assumed to occur in perpetuity. We are
also given that the corporate proﬁts are taxed at 36%, and that if this project were undertaken by an all—
equity ﬁrm, its cost of capital would be 20%. [1 point each for a total of 7 points]
r(UA) 2 0.2. investmentz$24m, Tc 2 3693‘ Sales 2 $30m. Costs = 75% of Sales
[1]: Work out the aftertax annual cash flow to the unlevered ﬁrm, [denoted UCF], and the NFV of the
project for the unlevered ﬁrm: '
With sales of $30m, costs of O.75*330m = 822.5m, pretax cash flow, denoted I, is
$7,5m. With tax rate of 36%, the atterotax Annual Cash flow. denoted UCF is $4.8m.
UCle'UTC): 4.8m. The NPV 2 24m + UCF/r(UA) 2 24m 4» 4.8m/02 2 0
ill}: If this project were undertaken by an unlevered ﬁrm. what would happen to the market value of the
unlevered ﬁrm? It would remain unchanged because the NPV is zero.
{ill}: Suppose the firm has a target debt to market value of assets ratio, [denoted TDA}. of 0.375. Work out
the amount of debt that would ensure that the target debt ratio is attained. TDA 2 0.3?5. Debt2TDA‘VUr’HT:;*TDA}:$10.404624277m [W]: Work out the APV [Adjusted NPV}. and VL [the value of the levered firm] with this amount of debt.
PVTS for debt2Tc'D 2$374566474m1 APV2NPV+PVTS2 3374566474m, V; : $24!”?! + APV 2 827.74566474m {V}: Assuming that the cost ofdeht capital is 10.8% work out the cost ofequity capital. thl’l TDA of 0.375. the debt wait be 8375 it the assets are sum. which means equity wall
be $62 5, THUS {35E 2 3353625 2 06. HS} 2 NBA} + {DfE} ‘ {l TK}'{1’{UA)4{D}}:20% +{BETH0.3610208.l08)2 23.53286b {VI}: New. work out the weighted average cost of capital, riWACC):(E‘VL)’r(E)+(DfVL)'f{D)'{1 T3) : (0625)“??353289’9 + (0.375)”10.8%'(10.36)
z 173% {Vii}: Discounting the UCF at the weighted average cost of capital, Show that you get the some answers for
the MW of the project from the perspective of the levered ﬁrm and for the trains of the levered ﬁrm as you
did to {IV} above. Note that in part [IV], we deﬁed the NPV of the project APV because that was the: method we were using in that part. VL = UCFM WACC) : $4.8m/O.173 = $27.74566474m L? The assets of ABC Inc. and XYZ Inc. are: identicai. ABC Inc. is an alldequity ﬁrm with I miliion shares
outstanding. The weighted average cost of capital for XYZ Inc. is 15%. The equity to debt ratio of XYZ is
0.93%, and its debt has been issued at 6.5%. The Stock of XYZ is vafued at $25, and XYZ has 8 million shares outstanding If the corporate income is taxed at 34%, work out:
[2 points for each part, 10 points for the entire question] (a): the cost of equity capital for XYZ, Inc, (b): the cost of capital for ABC Inc, (c): the price of the stock of ABC Inc. (d): the amount of the debt of XYZ, and (e): the present value of the m shield for XYZ, Inc. ABC is umevered, and is denoted as Firm U. XYZ is Ievered and is denoted as Firm L.
Given #(s)U : 1,000,000. r(WACC) 2 15%. EI’D : 0.9375 9 DfE : 1.0667, This means
that for every dollar of debt, equity contributes $09375, so that assets worth $19375
can be purchased. Thus, D/VL : 1/1 .9375 = 0.516. and EM = 0.9375/19375 = 0.484. We are also given that T( : 34%, that r(D) : 6.75%, that nyz : $25 and that #(sh
8,000,000, from which we can conciude that the market value of Firm L’s equity, E
$25*8m = SQOOm. With E/VL 2 0.9375/19375 : 0.483871, VL = $200m/O.483871 : 5341333333333, and D
= $213,333,33833. H H (a) We know r(WACC) MD). DNL ENL. and TC. From these we can figure out r(E) using
the formma for r(WACC).
15%:r(WACC):(E/VL)’r(E)+(D/VL)*r(D)*(1T¢;):(0.484)*r(E)+(0.516)*6.75%‘(1—0.34). (b) Now that we know r(E), r(D). and (Dz‘E) we can figure out rtUA) from the iormuia for
r(E).
26.248%:r(E)—r(UA}+(D/EfmUA)r(D)*(1TC):r(UA)+(1.0666)*(1—0.34)*(r(UA)—0,0675)
9 «um : 31% 31 (c) We know that VL = $413,333,33}'and that VL = VU + TC‘D ) VU : VL — TC'D
$413.33m ~ 0.34*8213.33m = $340.80m. Since ABC has 1m shares outstanding PM;
83408. (d) With EN! = 09375519375 : 0.483871. Vt 2 S200m£0483871 : $413,333.33333.
and D : $213,333.33333. (e): T, ‘D : 03432133307 2 87253301 II 3 ...
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 Spring '10
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