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FNCE – 3301
Corporate Finance Dr. Dante Suarez
Spring 2023
Homework 6 and TVM review
- Consider the following cash flows: Cash Flows ($) C 0 C 1 C 2 −7,850 5,600 20, a. Calculate the net present value of the above project for discount rates of 0, 50, and 100%. 0%: $17,950 100%: 0 50%: $4,861. b. What is the IRR of the project? 100%
- You have the chance to participate in a project that produces the following cash flows: Cash Flows ($) C 0 C 1 C 2
3, 5,800 –10, a. The internal rate of return is 11.15%. If the opportunity cost of capital is 10%, what is the NPV of the project? First, let’s try to answer the problem with the original numbers. This forces you to think about what the IRR and K of the project are, and how they relate to each other. If “the opportunity cost of capital”, your discount rate, is 10%. Then the NPV is -3,200 + 5,800/1.1 – 10,400/(1.1)^2 = -6, With the numbers as they should have been, then: -3,200 - 5,800/1.1 + 10,400/(1.1)^2 = 122 b. Would you accept the offer? As the numbers were (mis) spelled for you originally then you should not accept the project. As they should have been, then yes, you accept the project.
- Consider the following two projects: Cash flows Project A Project B C 0 −$^250 −$^250
C 1 105 133 C 2 105 133 C 3 105 133 C 4 105 a. If the opportunity cost of capital is 7%, which of these two projects would you accept (A, B, or both)? Both projects are acceptable, since their NPV is greater than 0 b. Suppose that you can choose only one of these two projects. Which would you choose? The discount rate is still 7%. Project A has a higher NPV, so you should choose that one c. Which one would you choose if the cost of capital is 13%? At a discount rate of 13%, then project B has a higher NPV d. What is the payback period of each project? Project A has a payback period of 2.38 years, while Project B has a payback period of 1. years e. Is the project with the shortest payback period also the one with the highest NPV? Not when the discount rate is 7% f. What are the internal rates of return on the two projects? A IRR 25%, B IRR 28% g. Does the IRR rule in this case give the same answer as NPV? Yes 4.The Cochinelle company is considering an investment in a new metal welder that will last 10 years. If the new welder is purchased, revenues will increase by $5,000 per year and cash operating costs will decline by $10,000 per year. The machine will cost $60,000, plus $10,000 in installation, and an increase in net working capital of $5,000; and will be depreciated on a straight-line basis over 6 years. While fully depreciated, at the end of its lifetime, the welder is estimated to have a salvage value of 10,000. Cochinelle’s marginal tax rate is 35% Determine the annual cash flows generated by the proposed project for years 0, 3, and 10. Year 0: -$75, Year 3: $8,
- Present Value of a Perpetuity Given variables are: payment per period (C ), interest rate (r ), and growth rate (g), and you solve for present value using: Perpetuity PV = C /(r-g) Note: when the payment per period is constant over time, then the growth rate g =0, the formula becomes Perpetuity PV = C /r Variations on a Theme: You may also need to solve for r, t or C. In every question, there will be three given variables and one unknown ... That's all! TVM problems can appear to be extremely complicated sometimes, because they can be the combination of several basic problems! There are many possible combinations, hence, it is not surprising to have a problem you never see before. But, remember, there are only five possible basic problems you can solve, and hence, it is just a matter of dividing large and complicated problems into several smaller and basic problems. How to figure out the correct rate (r) to use In TVM questions, which r to use is determined by the frequency of cash flow (C). For example, if the cash flow is occurring at yearly frequency, you will need an annual rate; if the cash flow is occurring at monthly frequency, you will need a month rate (i.e. mortgages and auto loans as examples); if cash flow is occurring at semi-annual frequency, you will need a semi-annual rate. Given APR, here is how you figure out monthly (quarterly, semi-annually) rate: Monthly r = APR/ 12 Quarterly r = APR / 4 Semi-annual r = APR / When we have annual cash flows and need an annual rate, the situation can be tricky. The reason is that we have two annual rates to choose from, one is APR and the other is EAR. APR assumes annual compounding, while EAR allows for more frequent compounding. Then the key to decide which rate out of the two to use is to look at the compounding frequency. If the compounding frequency is annual, then use APR as our rate (r). If the compounding frequency is more often (i.e., monthly, semi-annually, quarterly and etc.), we will need to use EAR. Given APR, here is how you figure out EAR Semi-annual compounding: EAR =( 1 + APR
2
Monthly compounding: EAR =( 1 + APR
12
Quarterly compounding: EAR =( 1 +^ APR
4
- Your company anticipates the introduction of environmental protection laws in three years time. Under these
laws you will have to pay a yearly environmental tax of $5,000, an obligation that will continue indefinitely. If the prevailing interest rate is 6% per year what is the present value of your company’s obligations under this law (the first payment will be four years from now)? $83,333.
- You are going to receive $1000 at year end per year for the next five years. The quoted APR is 5% compounded semi-annually. What is the present value of this annuity? $4645.
- Suppose you enter into a loan agreement to borrow $90,000 to help finance the purchase of your new home. The agreement specifies a term of 20 years with monthly repayments determined at a fixed rate of 9% per year (APR). (compounded monthly). (a) What is the amount of your monthly repayments? $4862. (b) Now suppose that exactly five years have passed (you made the 60th repayment yesterday). A rival lender offers to refinance your loan at a fixed rate of 8% APR. (compounded monthly). Costs associated with this refinancing amount to $1,500. Should you refinance? No Homework 7: TVM review Multiple Choice Questions i) Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to generate a 10-year stream of benefits amounting to $17,700 per year. The compound annual rate of return Comet expects to earn from this equipment is nearest: a. 17.7%
b. 12.0%
c. 10% d. 20% ii) An insurance company offers you ordinary annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9 percent. The present value of that annuity is nearest: a. $960, b. $438,144 (this was done using the tables, the excel calculation provided is actually more precise) c. $358, d. $359,
