Time Influence on Valuation - Review Questions Flashcards
Mark is basing his investment planning on a 15% return. His portfolio began with $7,000. At the end of the holding period, he had $8,256, including reinvested dividends. How did his portfolio do compared to his requirement of 15%?
r = (82567000)
− 1 = .18 or 18%. So Mark should be happy because his portfolio return was 3% better than his required return. At 15% return, Mark would have had a terminal value of 8050 = beginning value of 7000 x 1.15 = $8,050.
IRR Calculations from CFP Board released questions December 1996.
Smith invests in a limited partnership which requires an outlay of $9,200 today. At the end of years 1 through 5, he will receive the after-tax cash flows shown below. The partnership will be liquidated at the end of the fifth year. Smith is in the 28% tax bracket.
YEARS CASH FLOWS
0 ($9,200) CF0
1 $600 CF1
2 $2,300 CF2
3 $2,200 CF3
4 $6,800 CF4
5 $9,500 CF5
The after-tax IRR of this investment is
1) 17.41%
2) 19.20%
3) 24.18%
4) 28.00%
5) 33.58%
3) 24.18%
On the financial calculator, enter negative $9,200 as the initial cash flow. Then enter the remaining positive cash flows at the end of the years 1, 2, 3, 4, and 5, as indicated in the problem. The internal rate of return is 24.18%. Since the cash flows are identified as being after-tax flows, the tax bracket is irrelevant.
Which of the following statements is/are correct?
(1) The IRR is the discount rate which equates the present value of an investment’s expected costs to the present value of the expected cash inflows.
(2) The IRR is 24.18% and the present value of the investment’s expected cash flows is $9,200.
(3) The IRR is 24.18%. For Smith to actually realize this rate of return, the investment’s cash flows will have to be reinvested at the IRR.
(4) If the cost of capital for this investment is 9%, the investment should be rejected because its net present value will be negative.
(2) and (4) only
(2) and (3) only
(1) only
(1), (2) and (3) only
(1) and (4) only
(1), (2) and (3) only
(1) is correct as IRR is the rate of return that equates the present value of a project’s inflows with the present value of its outflows, thereby producing a net present value of zero. (2) is correct, by definition as the IRR. If the inflows are discounted at the 24.18% rate, they will produce a present value that is equal to the present value of the one outflow of $9,200. (3) is correct as it is an assumption of the internal rate of return methodology that any cash flow is reinvested at the IRR. (4) is incorrect. If we enter 9 as the interest rate, the calculation gives a positive $5,976.77.
What would happen if subsequent analysis showed that the appropriate YTM is actually greater than the YTM?
Choose the best answer.
1) Bond is undervalued
2) Bond is fairly priced
3) Bond is overvalued
3) Bond is overvalued
YTM*>YTM, then the bond is overvalued.
The capitalization method is applied to a bond valuation by comparing the bond’s yield-to-maturity (y) with the appropriate yield-to-maturity (y*) or required rate of return.
Specifically there are three criteria available for bond analysis:
If y > y, the bond is undervalued
If y < y, the bond is overvalued
If y = y*, then the bond is said to be fairly priced
An investment opportunity that cost $250,000 will provide cash flow of $40,000/year over the next 7 years. If the appropriate discount rate for this investment is 8%, what is the NPV for this investment? Is it a favorable investment?
NPV = $40,000(PVIFA 8%,7) − $250,000 = -$41,745.20; since it is negative, it is not favorable. (Financial calculator: 0 FV, 7 N, 8 I, 40000 PMT, PV = -208,254.80) or (208,254,80 - 250,000 = -41,745.20)
What is the duration of a 20-year bond with 8% annual coupon and an YTM of 7%?
Answer: 11.05 years
D=(1+YTM) / YTM − (1+YTM)+Duration(Coupon−YTM) / Coupon[(1+YTM)Duration−1]+YTM=
D=1+.07 / .07−(1+.07)+20(.08−.07) / .08[(1+.07)20−1]+.07=11.05 years
What would the duration be if it was a 30-year bond with 8% coupon and an YTM of 7%?
Answer: 13 years
D=(1+YTM) / YTM − (1+YTM)+Duration(Coupon−YTM) / Coupon[(1+YTM)Duration−1]+YTM=
(1+.07) / .07 − (1+.07)+30(.08−.07) / .08[(1+.07)30−1]+.07=12.9985or13years
What would the duration be if it was a 30-year bond with 12% coupon and an YTM of 11%?
Answer: 9.58 years
D=(1+YTM) / YTM − (1+YTM)+Duration(Coupon−YTM) / Coupon[(1+YTM)Duration−1]+YTM=
=(1+.11) / .11 − (1+.11)+30(.12−.11) / .12[(1+.11)30−1]+.11=9.5758or9.58years
Did you notice what was time’s influence on duration between the 20-year and 30-year bond? How about the influence of the size of the coupon on duration?
The longer the time, the greater the duration. Also, the greater the coupon, the lower the duration.
If a financial planner thinks that interest rates are going to fall soon, which action should he or she most likely take?
1) Buy bonds with short durations.
2) Buy bonds with long durations.
3) Sell bonds with long durations.
4) Do not buy bonds at all.
2) Buy bonds with long durations.
Bonds with long durations are more volatile than those with short durations. If interest rates are expected to fall, long-duration bonds will provide more capital appreciation than short-duration bonds. Therefore, long-duration bonds should be purchased.
Assume that a bond with a 5% yield to maturity has a modified duration of 7.56 years. Also assume that the discount rate for similar bonds rises to 5.75%. Based on the concept of modified duration, the bond’s price ought to change by:
1) 1.41%
2) -2.65%
3) -5.40%
4) -4.56%
3) -5.40%
The % change = -duration x [increase in interest rate/(1+old yield)]. In this case, % change= -7.56 x (0.75%/1.05)= -5.40%.
Which of the following bonds would be chosen to maximize return if interest rates are expected to decline?
1) Long-term bonds
2) Short-term bonds
3) Low-coupon bonds
4) High-coupon bonds
(1) and (3) only
(2) and (4) only
(2) and (3) only
(3) and (4) only
(1) and (3) only
A bond with a low (or zero) coupon and a long time until maturity will result in a longer duration and high price volatility, which will result in the largest capital gain when interest rates fall.
A 4% preferred stock was purchased for $80 per share. If interest rates are currently at 3% in the broad market, what is the value of this preferred stock as a perpetuity?
1) $80
2) $100
3) $106.67
4) $128.20
3) $106.67
To calculate the value of a bond or preferred stock in perpetuity, divide the payment by the prevailing interest rate: 3.2/.03= $106.67
A common stock just paid a dividend of $2.50. Dividends are projected to grow at 8%. What is its price if the market rate of return is 16%?
1) $17.67
2) $31.25
3) $33.75
4) $36.25
3) $33.75
Using the constant dividend growth model, V= d1/(r-g). First, find d1= [d0 x
(1+g)]= $2.50 x (1.08)= $2.70. V = $2.70/(.16- .08)= $33.75.
James uses dollar-cost averaging to purchase XYZ Corporation stock. He invested $12,000 initially and $3,000 at the end of each year for five years. The market value of the stock was $30,000 at the end of five years. What IRR did James earn on his investment?
1) 2.25%
2) 3.16%
3) 5.89%
4) 6.54%
2) 3.16%
The following keystrokes are utilized to find the IRR on the HP 12C calculator:
g, END
5, n
12000, CHS, PV
3000, CHS, PMT
30000, FV
i
The calculator gives an IRR of 3.16%
