Smeal College of Business Taxation and Management Decisions: ACCTG 550Pennsylvania State University Professor HuddartExam Review(1) Prove that when n =2,Savings Vehicle II generates a larger after-tax accumulation that Savings Vehicle I. What is the difference inaccumulations? Your answer should be in terms of t and R.Answer:SV II − SV I =(1 + R)2(1 − t)+t−(1 + R − Rt)2=[1+2R + R2− t − 2Rt − R2t + t]− [1 + R2+ R2t2+2R − 2Rt − 2R2t]= R2t − R2t2=(1− t)R2t> 0aslong as 0 <t<1.(2) Suppose Gypsy, age 25, makes one tax-deductible $2,000 contribution ofher salary to an IRA. Her investment (taxable corporate bonds) earnsa 12% annual return, and she liquidates the investment 10 years laterwhen she buys a house. Her ordinary tax rate is 25%, but she must paya 10% penalty tax since she liquidates the IRA before she reaches age5912.a. After taxes, how much cash does she have when she liquidates herIRA?Answer: When she liquidates, she has$2,000(1.12)10(1 − .35)=$4,038.b. Was it a mistake for Gypsy to set up an IRA?Answer: No. Had Gypsy not set up the IRA, she wouldhave accumulated only$2,000(1 − 25%) 1+.12(1 − .25)10=$3,551.cSteven Huddart, 1995–2005. All rights reserved. www.smeal.psu.edu/faculty/huddartACCTG 550 Exam Review(3) A corporation can invest in a tax-exempt municipal bond that yields 9%,a U.S. Treasury bond that yields 12%, or preferred stock with a 10%dividend yield. Each investment is riskless. Assume the corporation iseligible for a 70% dividends received deduction on the dividends. Whatis the tax clientele for the preferred stock? That is, corporations facingwhich tax rates will prefer the preferred stock over either the TreasuryBond or the municipal bond?Answer: For the corporation to prefer preferred stock, itmust be that .10(1−.3t) >.09 and .10(1−.3t) >.12(1−t).These equations simplify to 22.2% <t<33.3%.(4) What is the expected marginal tax rate of a firm in an NOL positionthat expects its NOLs to expire in four years half the time and fiveyears half the time, assuming its after-tax discount rate is 8% and itsstatutory tax rate is 34%?Answer:.5.34(1.08)4+ .5.34(1.08)5=24.07%.(5) Newco can invest $110,000 in R&D to build a solar gizmo at the startof year 1. The investment is sure to generate $300,000 at the end ofyear 12. Newco uses a 7.5% after-tax discount rate to evaluate projects.The corporate tax rate is 40%. Newco has no other sources of taxableincome. R&D is tax-deductible and generates a 10% tax credit. Incomeis taxed when received and expenses are deductible when paid.a. What is the NPV of this investment to Newco?Answer: Income in year 12 = $300,000. Tax in year 12= .4($300,000−$110,000)−$11,000 = $65,000.$235,000(1.075)12=$98,666, so NPV = $98,666 − $110,000 = −$11,334.b. Oldco is identical to Newco, except Oldco has $500,000 of taxableincome every year from its other operations. What is the NPV ofthis project to Oldco?Answer: All deductions and credits can be used imme-diately, so the after-tax cost is .6($110,000) − $11,000 =Page 2Exam Review ACCTG 550$55,000 in year 1.$180,000(1.075)12= $75,574, so NPV = $20,574.(6) Gary Kasparov invests $1,000 in an R&D limited partnership. All in-vested capital is spent on R&D expenditures in year 1. R&D expendi-tures are tax deductible and generate a 10% tax credit. Assume thatsuch credits may only be applied against income from the partnership. Ifthe project is a failure (60% probability), the partnership will liquidatein year 1, no cash will be distributed to the partners, and Gary’s shareof the partnership’s loss in year 1 will be $1,000. If the partnership is asuccess (40% probability), it will distribute $200 in cash to the partnersin perpetuity. If this occurs, Gary’s year 1 net loss from the partnershipwill be $800, and subsequent net income will be $200 per year. Gary’sonly other source of income is his salary from his job. If Gary faces a30% tax rate and uses an 8% after-tax discount rate in evaluating theproject, what is the expected net present value of this investment? As-sume the investment is made on January 1 and all cash inflows and taxpayments occur on December 31.Answer: If the project is a failure, Gary gets a $1,000deduction on December 31, which saves $300 in taxes; thecredit is suspended indefinitely. If the project is a success,Gary uses the deductions and credits to eliminate the taxon the income from the project until the deductions andcredits are fully used. This reduces the taxes from $60 to$0 in years 1 through 6, and from $60 to $20 in year 7.Thus the cash flows are:.63001.08+ .4200.08− .4201.087− .460.08 × 1.087= 987.The Expected NPV of the project is −$13.Page