Reference no: EM132250759

Assignment - Finance Questions

Part A -

Q1. Indicate which of the following statements about risk-free bonds are true and which are false. You do not need to show your work or explain your answers.

(a) Suppose bond A and bond B are both 10-year coupon bonds with a face value of $1,000 and annual coupons. If the coupon rate of bond A is greater than that of bond B, then the price of bond A is always greater than that of bond B.

(b) Suppose the term structure of interest rates is downward-sloping. Then the yield on a one-year zero-coupon bond is greater than that of a two-year coupon bond with an annual coupon.

(c) If the term structure is upward-sloping, investors expect the one-year interest rate to be higher one year from now than it is today.

(d) If the term structure is downward-sloping, then the forward rate f₂ is negative.

(e) A 10-year coupon bond has a face value of $1,000, an annual coupon rate of 5%, and a yield of 5%. If you buy this bond now and you sell it one year later, the internal rate of return on your investment is always 5%.

Q2. Suppose that the CAPM holds. Indicate which of the following statements are true and which are false. You do not need to show your work or explain your answers.

(a) Suppose that two stocks have the same beta but a different volatility. Then the stock with the higher volatility has a higher expected return.

(b) If two stocks have the same Sharpe ratio, then they must have the same beta.

(c) If two stocks have the same correlation with the market, then they must have the same beta.

(d) If portfolio P is efficient and portfolio Q is not efficient, then the Sharpe ratio of portfolio P is grader than that of portfolio Q.

(e) If portfolio P is efficient and portfolio Q is not efficient, then the beta of portfolio P is greater than that of portfolio Q.

Q3. Consider the CAPM regression of the excess return of a stock, portfolio, or mutual fund on the excess return of the market: R_i,t - r_f,t = α_i + β_i(R_m,t - r_f,t) + ε_i,t. Indicate which of the following statements are true and which are false. You do not need to show your work or explain your answers.

(a) α_i measures the idiosyncratic risk of the stock.

(b) β_i measures the systematic risk of the stock.

(c) An alternative way to estimate β_i for a given stock i is to estimate the mean of the stock's excess return and divide it by the volatility of the market's return; we get the same value as the slope in the above regression.

(d) If we run this regression on a mutual fund i's excess returns, then the best estimate of the fund manager's skill is α_i.

(e) If you find that α_i is close to zero and β_i = 0.4 for a hedge fund, then this means that the fund's historical returns tend to be lower than those of the market when the market experiences large positive returns, and higher than those of the market when the market experiences large negative returns.

Q4. Amgen just reported earnings of $10.00 per share and just paid a dividend of $5.00 per share. The company expects reinvested earnings to return 20% forever, but expects the extent of its new investments to slow down. Specifically, the company plans to keep the same plowback ratio of 50% for this year and next year (i.e., today and at the end of year 1), but plans to reduce it to 10% starting at the end of year 2 and for every year after that.

Amgen's equity cost of capital is 8%. Calculate the expected dividend per share at the end of year 1 and year 2 (i.e., Div_i and Div₂), as well as the current share price of Amgen.

Q5. 3M operates in two broadly defined industries, Industrial Products and Health Care, which have asset betas of 0.80 and 0.55, respectively. 3M's debt-to-equity ratio is 60%, its debt beta is 0.20, and its equity beta is 1.08.

(a) Compute 3M's debt-to-value ratio.

(b) Compute the asset beta for 3M overall.

(c) Compute the fraction of 3M's value that comes from its Industrial Products division (i.e., the value of the Industrial Products division relative to the total value of 3M).

Part B -

Q1. Anna is turning 25 today. She decides that she will start saving towards the purchase of a house that she wants to buy on her 30^th birthday. The kind of house that she wants to buy casts $400,000 today, but she expects this price to grow by 2% per year.

Anna has heard that a local bank offers a savings account paying an annual percentage rate (APR) of 6%, compounded monthly. For the next five years, she plans to make monthly contributions to the savings account, with the first contribution of $1,000 to be made in one month and her last contribution to be made on her 30^th birthday. She also plans to increase the size of each contribution by 0.3% per month.

After making her last contribution, she will use the funds in the account as a down payment for the house, financing the balance with a mortgage. She expects to get a 30-year mortgage with equal monthly payments (the first of which to take place one month after her 30^th birthday) and an annual percentage rate (APR) of 8.4%, compounded monthly.

(a) How much of the house (i.e., what amount) will need to be financed through the mortgage?

HINT: You will need to use the growing annuity formula: PV = C/(r-g) [1 - ((1+g)/(1+r))^T].             

(b) Assuming that she is correct about the interest rate of the mortgage, what will be the amount of her monthly payment?

Q2. You are given the following information about two U.S. government bonds that make annual payments.

Bond	Type	Face Value	Annual Coupon	Maturity	Price
A	Zero-Coupon Bond	$1,000	-	1 year	$985.22
B	Coupon-Bond	$1,000	9%	2 years	$1,126.15

(a) What are the 1-year and 2-year spot rates (r₁ and r₂)? (Show two decimal places, e.g., 1.23%) Is the term structure of interest rates upward-sloping or downward-sloping?

(b) What are the forward rates for year 1 and year 2 (f₁ and f₂)? (Show two decimal places, e.g., 1.23%).

(c) A third bond (Bond C) has a face value of $1,000, annual coupons, a coupon rate of 5%, and a 2-year maturity. It has a yield of 3%.

(i) What is the current price of Bond C.

(ii) Compute bond C's correct price, i.e., the price that the bond should have given the term structure of interest rates that you calculated in part (a).

(iii) Suppose that you buy bond C at its current price and the price adjusts to its correct level the next day. What is the one-day return that you would make on the investment?

Q3. Suppose that the global market portfolio consists of a portfolio of U.S. stocks (portfolio U) and a portfolio of non-U.S. stocks (portfolio N). Suppose that the CAPM holds with the market being the global market portfolio.

The portfolio of U.S. stocks has an expected return r_U = 8% and the portfolio of non-U.S. stocks has an expected return r_N = 10.5%. The standard deviations are σ_U = 20% and σ_N = 30%, and the correlation between the two is ρ_UN = 0.6. Finally, the risk-free rate is 3%.

Assume that the composition of the (global) market portfolio has a weight of 60% in the portfolio of U.S. stocks and 40% in the portfolio of non-U.S. stocks.

(a) Compute the expected return on the (global) market portfolio (r_m), the standard deviation of the (global) market portfolio (σ_m), and the Sharpe ratio of the (global) market portfolio (SR_m).

(b) Determine the beta of the portfolio of U.S. stocks (β_U), the beta of the portfolio of non-U.S. stocks (β_N), and the beta of the (global) market portfolio (β_m).

(c) Your client has $100 million invested, 80% of which is in the portfolio of U.S. stocks, and the rest in risk-free assets. What is the expected return r_p, volatility σ_p, Sharpe ratio SR_p, and beta β_p of your client's portfolio?

(d) Keeping the volatility of her portfolio the same, can your client achieve a higher expected return? If so, what portfolio do you advise your client invest in? Compute the expected return r_ep of that portfolio, as well as its Sharpe ratio SR_ep, and beta β_ep. How much money will your client invest in the risk-free asset, the portfolio of U.S. stocks, and the portfolio of non-U.S. stocks if she follows your advice?

Q4. Hilcorp Energy, founded in 1989, is one of the largest privately-held oil and natural gas exploration and production companies in the United States. Hilcorp is contemplating an Initial Public Offering (IPO) of equity shares, and you have been hired to advise its founder and CEO, Jeffery Hildebrand, about the value of the firm.

The firm's CFO has produced the following pro forma income statement for the next two years of the firm. (Assume that time 0 (today) is 2018, time 1 is 2019, etc., and that all figures are in $million.]

	2018	2019	2020
Sales Revenue	-	540	600
Cost of Goods Sold (COGS)	-	400	450
Selling, General & Administrative (SG&A)	-	20	30
Depreciation	-	70	60

In addition, the CFO expects the firm's current Net Working Capital of $40 million to increase to $50 million in 2019 and to $58 million in 2020. Finally, Hilcorp expects to make new investments in long-term assets of $50 million in 2019 and $40 million in 2020.

To do the valuation, you have gathered data on comparable oil and gas companies that are publicly traded, Tesoro Corporation (TSO) and Valero Energy Corporation (VLO).

	TSO	VLO
EBITDA in 2018 (in $millions)	3,200	6,520
Debt (D, in $millions)	6,000	6,000
Equity (E, in $millions)	10,000	24,000
Debt Beta (βD)	0.32	0.00
Equity Beta (βE)	2.08	1.60

The corporate tax rate is 40%. The risk-free rate is 2.9%, and the market risk premium is 6%.

(a) Calculate the proper discount rate for Hilcorp.

(b) Calculate Hilcorp' free cash flows for 2019 and 2020.

(c) You decide to estimate the 2020 terminal value (TV₂₀₂₀) using an EBITDA multiple estimated from the two comparable firms.

(i) What is your estimate of TV₂₀₂₀?

(ii) In words, what does this terminal value represent?

(iii) What is the perpetual growth rate in free cash flows that is implicitly imbedded in this terminal value? [Hint: Calculate this growth rate assuming that the free cash flows would start growing at a rate g from the free cash flow in 2020]

(iv) What is the value of Hilcorp (in 2018) based on the above analysis?