STUDY QUESTIONS - ENGR 111 – Fall 2011 STUDY...

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Unformatted text preview: ENGR 111 – Fall 2011 STUDY QUESTIONS: 1. You are considering a new product launch. The project will cost $960,000, have a four year life, and have no salvage value. Depreciation is straight line to zero. Sales are projected at 240 units per year, price per unit will be $25,000; variable cost per unit will be $19,500; and fixed costs will be $830,000 per year. The required rate on the project is 15%, and the relevant tax rate is 35%. a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within +/ ­ 10%. What are the upper and lower bounds for these projections? What is the base case NPV? What are the best case and worst case scenarios? b. Evaluate the sensitivity of your base case NPV to changes in fixed costs. c. What is the accounting break ­even level of output for this project? ANSWER: a. The base ­case, best ­case, and worst ­case values are shown below. Remember that in the best ­case, unit sales increase, while costs decrease. In the worst ­case, unit sales, and costs increase. Scenario Base Best Worst Using the tax shield approach, the OCF and NPV for the base case estimate are (where PVIFA15%,4 stands for the present value factor for fixed annuity, that is, the discounting factor for the next four years at 15%): OCFbase = [($25,000 – 19,500)(240) – $830,000](0.65) + 0.35($960,000/4) OCFbase = $402,500 NPVbase = –$960,000 + $402,500(PVIFA15%,4) NPVbase = $189,128.79 The OCF and NPV for the worst case estimate are: OCFworst = [($25,000 – 21,450)(216) – $913,000](0.65) + 0.35($960,000/4) OCFworst = –$11,030 NPVworst = –$960,000 – $11,030(PVIFA15%,4) Unit sales Variable cost Fixed costs 240 $19,500 $830,000 264 $17,550 $747,000 216 $21,450 $913,000 NPVworst = $991,490.41 And the OCF and NPV for the best case estimate are: OCFbest = [($25,000 – 17,550)(264) – $747,000](0.65) + 0.35($960,000/4) OCFbest = $876,870 NPVbest = –$960,000 + $876,870(PVIFA15%,4) NPVbest = $1,543,444.88 b. To calculate the sensitivity of the NPV to changes in fixed costs, we choose another level of fixed costs. We will use fixed costs of $840,000. The OCF using this level of fixed costs and the other base case values with the tax shield approach, we get: OCF = [($25,000 – 19,500)(240) – $840,000](0.65) + 0.35($960,000/4) OCF = $396,000 And the NPV is: NPV = –$960,000 + $396,000(PVIFA15%,4) NPV = $170,571.43 ΔNPV/ΔFC = ($189,128.79 – 170,571.43)/($830,000 – 840,000) ΔNPV/ΔFC = –$1.856 For every dollar FC increase, NPV falls by $1.86. c. The sensitivity of NPV to changes in fixed costs is: The accounting breakeven is: QA = (FC + D)/(P – v) QA = [$830,000 + ($960,000/4)]/($25,000 – 19,500) QA = 194.55 or about 195 units 2. The Faulk Corp. has a 6 percent coupon bond outstanding. The Gonas Company has a 14 percent bond outstanding. Both bonds have 8 years to maturity, make semi ­annual payments and have a yield to maturity of 10 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these two bonds? What if the interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bond? ANSWER Initially, at a YTM of 10 percent, the prices of the two bonds are (where PVIFA5%,16 is as defined in Question 1): PFaulk = $30(PVIFA5%,16) + $1,000(PVIF5%,16) = $783.24 PGonas = $70(PVIFA5%,16) + $1,000(PVIF5%,16) = $1,216.76 If the YTM rises from 10 percent to 12 percent: PFaulk = $30(PVIFA6%,16) + $1,000(PVIF6%,16) = $696.82 PGonas = $70(PVIFA6%,16) + $1,000(PVIF6%,16) = $1,101.06 The percentage change in price is calculated as: Percentage change in price = (New price – Original price) / Original price ΔPFaulk% = ($696.82 – 783.24) / $783.24 = –0.1103 or –11.03% ΔPGonas% = ($1,101.06 – 1,216.76) / $1,216.76 = –0.0951 or –9.51% If the YTM declines from 10 percent to 8 percent: PFaulk = $30(PVIFA4%,16) + $1,000(PVIF4%,16) = $883.48 PGonas = $70(PVIFA4%,16) + $1,000(PVIF4%,16) = $1,349.57 ΔPFaulk% = ($883.48 – 783.24) / $783.24 ΔPGonas% = ($1,349.57 – 1,216.76) / $1,216.76 = +0.1092 or 10.92% All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates. = +0.1280 or 12.80% 3. You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $800 a month in a stock account in real dollars and $400 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an 8 percent effective return. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25 ­year withdrawal period? What is the nominal dollar amount of your last withdrawal? ANSWER h: inflation rate EAR: Effective Annual Rate To answer this question, we need to find the monthly interest rate, which is the APR divided by 12. We also must be careful to use the real interest rate. The Fisher equation uses the effective annual rate, so, the real effective annual interest rates, and the monthly interest rates for each account are: Stock account: (1 + R) = (1 + r)(1 + h) 1 + .12 = (1 + r)(1 + .04) r = .0769 or 7.69% APR = m[(1 + EAR)1/m – 1] APR = 12[(1 + .0769)1/12 – 1] APR = .0743 or 7.43% APR = 12[(1 + .0288)1/12 – 1] APR = .0285 or 2.85% Monthly rate = APR / 12 Monthly rate = .0743 / 12 Monthly rate = .0062 or 0.62% Bond account: (1 + R) = (1 + r)(1 + h) 1 + .07 = (1 + r)(1 + .04) r = .0288 or 2.88% APR = m[(1 + EAR)1/m – 1] Monthly rate = APR / 12 Monthly rate = .0285 / 12 Monthly rate = .0024 or 0.24% Now we can find the future value of the retirement account in real terms. The future value of each account will be: Stock account: FVA = C {(1 + r )t – 1] / r} FVA = $800{[(1 + .0062)360 – 1] / .0062]} FVA = $1,063,761.75 Bond account: FVA = C {(1 + r )t – 1] / r} FVA = $400{[(1 + .0024)360 – 1] / .0024]} FVA = $227,089.04 The total future value of the retirement account will be the sum of the two accounts, or: Account value = $1,063,761.75 + 227,089.04 Account value = $1,290,850.79 Now we need to find the monthly interest rate in retirement. We can use the same procedure that we used to find the monthly interest rates for the stock and bond accounts, so: (1 + R) = (1 + r)(1 + h) 1 + .08 = (1 + r)(1 + .04) r = .0385 or 3.85% APR = m[(1 + EAR)1/m – 1] APR = 12[(1 + .0385)1/12 – 1] APR = .0378 or 3.78% Monthly rate = APR / 12 Monthly rate = .0378 / 12 Monthly rate = .0031 or 0.31% Now we can find the real monthly withdrawal in retirement. Using the present value of an annuity equation and solving for the payment, we find: PVA = C({1 – [1/(1 + r)]t } / r ) $1,290,850.79 = C({1 – [1/(1 + .0031)]300 } / .0031) C = $6,657.74 This is the real dollar amount of the monthly withdrawals. The nominal monthly withdrawals will increase by the inflation rate each month. To find the nominal dollar amount of the last withdrawal, we can increase the real dollar withdrawal by the inflation rate. We can increase the real withdrawal by the effective annual inflation rate since we are only interested in the nominal amount of the last withdrawal. So, the last withdrawal in nominal terms will be: FV = PV(1 + r)t FV = $6,657.74(1 + .04)(30 + 25) FV = $57,565.30 ...
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This note was uploaded on 12/05/2011 for the course ENGINEERIN 111 taught by Professor Melihabulu-taciroglu during the Fall '11 term at UCLA.

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