# More Supplementary Notes – Ch

```ADMS 3530 Final Review Session – Solutions
Example 1: Multiple Cash Flows
Detailed solution:
0
1
2
|-----------|-------------I
\$200 “Y” 2400
r = 4%
FV2 = \$3032.32
You can use either
Option a) FV formula and bring all cash flows to t=2 or
Option b) PV formula and bring all cash flows to t=0
Option a) Bring all cash flows to t=2 (use FV or compound)
200(1 + r)2 + Y(1 + r)1 + 2400 = 3032.32
200(1.04)2 + Y (1.04) + 2400 = 3032.32
216.32 + Y(1.04) + 2400 = 3032.32
Y(1.04) = 3032.32 – 2400 – 216.32
Y(1.04) = 416
Y = 416 / (1.04)
Y = \$400
Option b) Bring all cash flows to t=0 (use PV and discount)
200 + Y/(1 + r)1 + 2400/(1 + r)2 = 3032.32/ (1 + r )2
Y = \$400.00
Example 2: Delayed Annuity
PMT = \$100, I = 9, n= 4, Fv =0, COMP PV
 PV = \$323.97 at t=1 !!
Bring PV1 to PV0
PV0 = \$323.97 / (1.09)1 = \$297.22
Example 3: EAR
Using your calculator: PMT = \$1883.33, n = 12, PV = \$20,000, FV=0, Comp “i”
 i= 1.9322%
EAR = (1+.019322)12 -1 = 25.82%
Example 4: Mortgages
3530_Final_Tutorial_-_Solutions Updated.docx
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The monthly interest rate is given by:
(1 + im )12 = 1 + EAR = (1 + 3125%)² = 1.076406, that is im = 0.5142%
The monthly payment for the 20-year loan
320,000 = PMT x PVIFA(0.5142%,300)
PMT = \$2,095.22
Mortgage remaining at the end of 5 years  240 months remaining:
PMt = \$2095.22, n=240, i=.5142, Fv=0, COMP PV
 PV = 288,480.10
Example 5: Bonds
Solution
a) Current Yield = Annual Coupon Payment/ Bond Price
Step 1: Find price of bond today (7 years remaining)
PMT = 70/2 = 35.00, n = 7 x 2 = 14, FV = 1000, i = 8/2 = 4%, COMP PV
 PV = -947.18
-> Current Yield = \$70/\$947.18 = 7.39%
Step 2: Find rate of return over holding period (3 years)
b.
Solution B
4-year Rate of Return = [30 x FVIFA(2%,8) + 1,040 – 1,015] / 1,015 = 27.8314% The annual
rate of return is (1+27.8314%)1/4 – 1 = 6.3309%
Example 6A: Stocks
DIV1  DIV0 (1.25 ); DIV2  DIV0 (1.25 ) 2 ;
DIV3  DIV0 (1.25 ) 3 ; DIV4  DIV0 (1.25) 3 (1.18 ).
DIV5 DIV4 (1  g ) DIV0 (1.25 3 )(1.18 )(1  0.08)
P4 


rg
rg
0.15  0.08
2.489 DIV0
 35.56 DIV0 .
0.07
DIV0 (1.25 ) DIV0 (1.25 ) 2 DIV0 (1.25) 3 DIV0 (1.25 ) 3 (1.18 ) 35.56DIV0
P0  \$60 




1.15
1.15 2
1.15 3
1.15 4
1.15 4
 DIV0 ( 25.2).

 DIV0 
\$60
 \$2.38  DIV1  \$2.38  1.25  \$2.975  \$2.98.
25.2
3530_Final_Tutorial_-_Solutions Updated.docx
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Example 7
Solution C
Step 1: Determine the initial cash outflow. The payback is 2.25 years, so the cash
flow will be:
CF0 = -[CF1 + CF2 + 0.25(CF3)]
= -[\$500 + \$300 + 0.25(\$400)]
= -\$900.
Step 2: Calculate the IRR:
CF0 = -900; CF1 = 500; CF2 = 300; CF3 = 400; CF4 = 600; and then solve
for IRR = 33.49% ≈ 33.5%
Example 7B
Step 1: Determine the differential cash flows between Projects A and B
Project A Project B ΔCFs
Year Cash Flow Cash Flow A - B
0 -\$2,000 -\$1,500 -\$500
1 700 300 400
2 700 500 200
3 1,000 800 200
4 1,000 1,100 -100
Step 2: Calculate the IRR of the differential cash flows
CF0 = -500; CF1 = 400; CF2 = 200; CF3 = 200; CF4 = -100; and then solve for
IRR = 26.67%
Example 7C
Choose the project that maximized your NPV
NPVI = 2,781.65
NPVII = 1,922.12
Choose project I.
Example 8 DCF
Beg UCC
Year 1 600,000
Year 2 510,000
CCA
90,000
153,000
CCA Tax Shield
31,500
53,550
End UCC
510,000
357,000
Example 9
From the PV CCA Tax Shield formula:
PVCCATS = [(600,000 x .30 x .35)/(.12 + .30)] x [(1 + 0.5 x 0.12)/(1.12)]
= 141,964
Example 10
After-tax CFO (excluding CCA) = 240,000 x (1 - 0.35) = 156,000
NPV = -600,000 + 156,000 x PVIFA(12%,4) + 141,964 = 15,791
3530_Final_Tutorial_-_Solutions Updated.docx
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Example 11
PVCCATS will decrease by: [(50,000 x .30 x .35)/(.12 + .30)] x (1.12)-4 = 7,944
PV(CFO excluding CCATS) will increase by 50,000 x (1.12)-4 = 31,776
So, NPV will increase by 31,776 – 7,944 = 23,832
Example 12A
1) In the best-case scenario:
The before-tax profit is
= 12,000(1+10%)\$21(1+5%) - 12,000(1+10%)\$11(1-3%) - \$44,000(1-1%) - \$40,000 = \$66,656.
The after-tax profit = \$66,656(1-34%) = \$43,992.96.
The operating cash flow = \$43,992.96 + \$40,000 = \$83,992.96.
The PV of the operating cash flow using an annuity factor of 12% for 2 years is
= \$141,952.39.
The NPV is = \$141,952.39 - \$80,000 = \$61,952.39.
2) In the worst-case scenario:
The before-tax profit is
= 12,000(1-10%)\$21(1-5%) - 12,000(1-10%)\$11(1+3%) - \$44,000(1+1%) - \$40,000 = \$8,656.
The after-tax profit = \$8,656(1-34%) = \$5,712.96.
The operating cash flow = \$5,712.96 + \$40,000 = \$45,712.96.
The PV of the operating cash flow using an annuity factor of 12% for 2 years is
= \$77,257.23.
The NPV is = \$77,257.23 - \$80,000 = -\$2,742.77.
3) The difference in the NPVs = \$61,952.39 – (-\$2,742.77) ≈ \$64,695.
Example 12B
Old price = \$60/1.2 = \$50.
Therefore, variable costs per product = \$50 × 0.7 = \$35, which equals 58.33% of
the new price. So the new accounting break-even revenue
= \$1 million / (1-0.5833)  \$2,400,000.
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Example 13A: Risk
The equal probability is 1/3.
The portfolio expected return = (1/3)(-4% + 2% + 5%) = 1%.
The portfolio variance = (1/3)[(-4%-1%)2 + (2%-1%)2 + (5%-1%)2]
= 14 percentages squared = 0.0014.
Taking the square root of the portfolio variance, we find that the portfolio standard deviation is
3.74%.
Example 13B: Risk
Correlation Coefficient:
 j ,m 
Portfolio standard deviation   P 
Cov(rj , rm )
 jm
= -0.016 / (.16 x.20) = -0.5
x12 12  x22 22  2 x1 x2 1, 2 1 2 , = 10.44%
Example 14 CAPM
Example 15 CAPM
Example 16 CAPM
Expected Return W = 6% + 2.0 x 9% = 24% < 25% => Buy W.
Expected Return X = 6% + 1.6 x 9% = 20.4% > 19% => Do not buy X.
Expected Return Y = 6% + 1.1 x 9% = 15.9% < 17% => Buy Y.
Expected Return Z = 6% + 0.8 x 9% = 13.2% > 11% => Do not buy Z.
Note: You should sell (short) X and Z because they are overpriced by the market
Example 16B
Project I: expected return = 0.06 + 2 × 0.09 = 0. 24 < IRR of 0.25.
 Project I plots above the SML and should be accepted.
Project II: expected return = 0.06 + 1.1 × 0.09 = 0. 159 > IRR of 0.15.
 Project II plots below the SML and should be rejected.
3530_Final_Tutorial_-_Solutions Updated.docx
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Example 17 WACC
FV=1000, PV=-860, N=20, PMT=45; I=? 5.69%  YTM=5.69 × 2 =11.38%.
After-tax cost of debt = 11.38% × (1-35%) = 7.40%.
By the CAPM: requity = 5.25% + 2 × 4.15% = 13.55%.
The annual dividend paid on per preferred share is \$100 × 5% = \$5.
So rpreferred = \$5 / \$63 = 7.94%.
Price
Shares (million)
Market Value (\$
million)
Weights
Costs
WACC
Equity
58
38
2,204
0.60
13.55%
11.22%
Preferred Debt
63
860
14
0.7
882
0.24
7.94%
Value
602
0.16
7.40%
3,688
Chap 20, 21 and 22 (consistent with the course outline)
Cash conversion cycle = (inventory period + accounts receivable period) – accounts
payable period
The implicit interest rate per month = \$(1,000,000-960,000)/\$960,000
= 4.1667%
12
The effective annual rate = (1+0.041667) -1=63.21%
3530_Final_Tutorial_-_Solutions Updated.docx
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E)
3530_Final_Tutorial_-_Solutions Updated.docx
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