CHAPTER 2
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507*1.126 = $1
2. 125/139 = .899
3. PV = 374/(1.09)9 = 172.20
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003
5. FV = 100*1.158 = $305.90
6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40
8. a. PV = 1/.10 = $10
b. Since the perpetuity will be worth $10 in year 7, and since that is roughly double the present value, the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)
c. A perpetuity paying $1 starting now would be worth $10, whereas a
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From this equation, we can solve for the amount to be put aside each year.
PV(boat) = $20,000/(1.10)5 = $12,418
PV(savings) = Annual savings
Because PV(savings) must equal PV(boat):
Annual savings
Annual savings
Another approach is to use the future value of an annuity formula:
Annual savings = $ 3,276
22. The fact that Kangaroo Autos is offering “free credit” tells us what the cash payments are; it does not change the fact that money has time value. A 10% annual rate of interest is equivalent to a monthly rate of 0.83%: rmonthly = rannual /12 = 0.10/12 = 0.0083 = 0.83%
The present value of the payments to Kangaroo Autos is:
A car from Turtle Motors costs $9,000 cash. Therefore, Kangaroo Autos offers the better deal, i.e., the lower present value of cost.
23. The NPVs are: at 5% at 10% at 15%
The figure below shows that the project has zero NPV at about 11%.
As a check, NPV at 11% is:
24. a. This is the usual perpetuity, and hence:
b. This is worth the PV of stream (a) plus the immediate payment of $100:
PV = $100 + $1,428.57 = $1,528.57
c. The continuously compounded equivalent to a 7% annually compounded rate is approximately 6.77%, because: e0.0677 = 1.0700
Thus:
Note that the pattern of payments in part (b) is more valuable than the pattern of payments in part (c). It is preferable to receive cash flows at the start of every year than to spread the
b. What is the present value of this annuity if the opportunity cost rate is 10% annually? 10% compounded semiannually?
Therefore the annual interest rate is 8% and the effective annual rate compounded quarterly is 8.24%
a) In the first set of calculations, the staff used a discount rate of 20%, a five-year time horizon, and ignored taxes and terminal value. What is the relative attractiveness of these three alternatives?
For the Chicago native Devonte Ingram he would have to step up in a life or death situation because when he was about to lose all he had left he held on. It was about 7:30 on a Monday night and Devonte walking a few steps in front of his sister (Diavonnie Ingram) when the unthinkable happened "I bent down to tie my shoe and then I felt something lift me up from the back of my book bag then tried to throw me in the van," said Diavonnie Ingram Devonte unknowingly walking ahead suddenly heard his sisters cry’s rushed into the rescue "I just had to pull her legs until I had started screaming and he had let go," Devonte Ingram said. Finally the man had let go but he wasn’t giving up "She had moved her arms so the book bag could slip off and then
10. An investment of $1,000 today will grow to $1,100 in one year. What is the continuously compounded rate of return?
15) A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of
b. How would you estimate the appropriate discount rate to be used in valuing the cash flows?
With a 35% tax, the alternative of selling of the vessel with a predicted total lifetime of 25 years, yields a slightly higher NPV compared to scraping after 15 years of use. The increase in NPV due to selling is because of a higher cash flow in the beginning of 2018 when the sale of the vessel occurs.
Which of the following is the actual rate of interest paid or earned over a year's time?
C) The cash flows for an annuity due must all occur at the ends of the periods.
a. Compute the rate for the current year. (Show your work for credit; 2 points)
A bank is offering you a credit card with an APR of 16%, compounded monthly.What is the Effective Annual Rate (EAR)? 17.23%
Edgar Allan Poe is known for the suspenseful and mysterious nature in his short stories, and to achieve this he uses repetitive symbolism. In the “Fall of the House of Usher”, the narrator gets a letter from an old friend saying that he needs his help. When he arrives he starts to hear voices that eventually cause the house to fall and results in the death of usher and Madeline. Poe's “The fall of the House of Usher” portrays a melancholy setting and utilizes a motif of the supernatural, however, the symbolism conveys the evil of the people and the house which ultimately revealing Poe's overwhelming prevalence of symbolism and fascination with the superstitions of his time.
D. Have no effect on either cash flows or risk because the cash flows are already reflected in the income statement
b. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?