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Evaluating Return and Cash Flow Streams 1 Evaluating Returns and Cash Flow Streams Adi’Yah Williams Capella University Problem 1: Portfolio Required Return

Evaluating Return and Cash Flow Streams 2 You are the money manager of a $10 million investment fund, which consists of four stocks. This fund has the following investments and betas: Stock Investment Beta A $3,000,000 1.50 B $1,000,000 (0.50) C $2,000,000 1.25 D $4,000,000 0.75 If the market's required rate of return is 12 percent, and the risk-free rate is 4 percent, what is the fund's required rate of return? Portfolio Beta: Stock A investment / investments + Beta A + Stock B investment / investment + Beta B + Stock C investment / investments + Beta C + Stock D / Investment + Beta D = Asset Weighted 3,000,000 / 10,000,000 = .30 x 1.50 +1,000,000 / 10,000,000 = .10 x (0.50) +2,000,000 / 10,000,000 = .20 x 1.25 +4,000,000 / 10,000.000 = .40 x .75 .30 x 1.50 + .10 x (0.50) + .20 x 1.25 + .40 x .75 .45 + (.05) + .25 + .30 = .95 Required Rate of Return: Risk-Free Rate + Asset Weighted .04 + .95 (.12 - .04) .04 + .95 (.08)

Evaluating Return and Cash Flow Streams 3 .04 + .076 The required rate of return is .116 = 11.6% Problem 2: Required Rate of Return ● Stock R's beta = 1.5 ● Stock S's beta = 0.75 Consider that the required return on an average stock is 14 percent. The risk-free rate of return is 6 percent. If this is so, the required return on the riskier stock exceeds the required return on the less risky stock by how much? Stock R's beta = 1.5 Risk-Free Rate + Stock R’s Beta .06 + 1.5 (.14 - .06) .06 + 1.5 (.08) .06 + .12 Stock R = .18 = 18% Stock S's beta = 0.75 Risk-Free Rate + Stock S .06 + .75 (.14 - .06) .06 + .75 (.08) .06 + .06 Stock S = .12 = 12% Stock R – Stock S .18 - .12

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Evaluating Return and Cash Flow Streams 4 .06 = 6% Required Rate of Return Different between Stock R and Stock S is 6% Problem 3: CAPM and Required Return Calculate the required rate of return for XYZ Inc. using the following information: ● Investors expect a 3.0 percent rate of inflation. ● The real risk-free rate is 2.0 percent. ● The market risk premium is 6.0 percent. ● XYZ Inc. has a beta of 1.7. ● Over the past 5 years, the realized rate of return has averaged 13.0 percent. .02 + .03 + 1.7 (.06) .02 + .03 + .102 .05 +.102 = .152 or 15.2% Over the previous five years, XYZ's RFR was 13%; however, there is a probability of 15.2%. Problem 4: Bond Valuation You have two bonds in your portfolio. Each bond has a face value of $1000 and pays an 8 percent annual coupon. Bond X matures in 1 year, and Bond Y matures in 15 years.

Evaluating Return and Cash Flow Streams 5 1. If the going interest rate is 4 percent, 9 percent, and 14 percent, what will the value of each bond be? Assume Bond X only has one more interest payment to be made at maturity. Assume there are 15 more payments to be made on Bond Y. ENTERED DATA ON ATTACHED EXCEL SHEET. 2. The longer-term bond's price varies more than the shorter-term bond's price when interest rates change. Explain why. Bond prices tend to decline in response to rising interest rates. Bonds with short maturities are less susceptible to rises in interest rates. The SEC states that "the general movement of bond prices and market interest rates is opposite" and that this is a fundamental premise of bond investing. They continued by saying that fixed-rate bond prices decrease as market interest rates rise. We call this phenomenon interest rate risk. Problem 5: Yield to Call Five years ago, XYZ Inc. issued 20-year bonds with a 12 percent annual coupon rate at their $1,000 par value. The bonds had 5 years of call protection and an 8 percent call premium. Yesterday, XYZ Inc. called the bonds. For this problem, imagine that the investor who purchased the bonds when they were issued held them until they were called. Considering this, compute the realized rate of return. Should the investor be happy with XYZ Inc. calling the bonds? Why or why not? Over the five years, investors have profited from the 20-year bond. Even though the investor would have made more money in 20 years, they could still turn a profit.

Evaluating Return and Cash Flow Streams 6 Pv=$1000, Coupon Rate= 12%, Coupon=$120, # of years=20, Callable years=5, and Call premium=8%. The bondholder was paid interest totaling $600 over five years (1000 x.12 x 5). When the bond is called in with an 8% premium, the bondholder will get $1,080 (1000 x.08) for the bond. They received a total return on their investment of $600 + $1,080 = $1,680. Interest rates must be considered if the bondholder buys more bonds, particularly callable bonds. They can only invest in bonds with that present rate if the interest rate has dropped. If the bond is callable, the issuer may call it at a higher interest rate than what was paid out throughout the bond's term, profiting from the difference. XYZ took the wise move to call the bonds before their 20-year maturity. They saved $1,800 for every bond sold, although paying $680 more than the initial bond purchase. The investor would have made much more money (1000 x.12 x 20) if XYZ had waited for the bonds to mature. The gain over 20 years would have been $2,400 plus the $1,000 par value, for $3,400. The investor would have made more money at current rates than the initial bond value. We can forecast the bond's worth for fifteen more years once it matures. Problem 6: Yield to Maturity XYZ Inc. bonds have 5 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 8 percent. 1. What is the yield to maturity at a current market price of (1) $800; and (2) $1,200? 2. If a "fair" market interest rate for such bonds was 12 percent—that is, is rd=12%— would you pay $800 for each bond? Why or why not?

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Evaluating Return and Cash Flow Streams 7 1: The yield to maturity at current price of $800 YTM= Rate ( 5,80,-800,1000) = 13.80% The yield to maturity at current price of $1200 YTM= rate(5,80,-1200,100) = 3.56% 2: The bond would be worth $855.81 then. With a five-year maturity date of $1,376 and a fair market interest rate of 12%, I would buy the bond for $800. Interest on a five-year bond would be $96 x 5 = $480. The bond will mature for $800 x 12%, or $896.00, plus $480 in interest paid thus far, or $1,376. Pv=$1,000 Coupon rate = 12 5 # of years=20 Callable years=5 Call premium =8% Problem 7: After-Tax Cost of Debt XYZ Inc.'s currently outstanding bonds have a 10 percent yield to maturity and an 8 percent coupon. It can issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 40 percent, what is XYZ's after-tax cost of debt? Weighted average cost of capital = After-tax cost = Interest rate on new debt – tax savings d - dT d(1-T) d(1-.40)= .60 or 60%

Evaluating Return and Cash Flow Streams 8 Marginal tax rate = 40% YTM = 10% 1.0-.40=.60 or 60% Problem 8: Present Value of an Annuity Find the present values of the following ordinary annuities if discounting occurs once a year: 1. $300 per year for 10 years at 10 percent. 2. $150 per year for 5 years at 5 percent. 3. $350 per year for 5 years at 0 percent. $300 x [1 – (1 + .10) ^ ¹ ] / .10 ⁻ ⁰ $300 x [1 – (1.1)^ ¹ ] /.10 ⁻ ⁰ $300 x (1-.3855) / .10 $300 x .6145 / .10 184.35 / .10 $300 per year for 10 years at 10%= $1,843.50 $150 x [1 – (1 + .05)^ ] / .05 ⁵ ⁻ $150 x [1 – (1.05)^ ] / .05 ⁵ ⁻ $150 x (1 - .7835) / .05 $150 x .2165 / .05 32.475 / .05

Evaluating Return and Cash Flow Streams 9 $150 per year for 5 years at 5%= $649.50 $350 x [1 – (1+.05)^ ] / .00 ⁻⁰ $350 x [1 – (1.05)^ ] / .00 ⁻⁰ $350 x 5 $350 per year for 5 years at 0% = $1,750.00 Problem 9: Uneven Cash Flow Stream Use the table below to answer the following: 1. What are the present values of the following cash flow streams if they are compounded at 5 percent annually? PV = [100 / (1 + .05)^¹] + [400 / (1 + .05)^²] + [400 / (1 + .05)^³] + [400 / (1 + .05)^⁴] + [300 / (1 + .05)^ ]⁵ [100 / (1.05)^¹] + [400 / (1.05)^²] + [400 / (1.05)^³] + [400 / (1.05)^⁴] + [300 / (1.05)^⁵ 100 / 1.05 + (400 / 1.1025) + 400 / 1.1576 + (400 / .1.2155) + 300 / 1.2762 95.238 + 362.811 + 345.542 + 329.082 + 235.072 = $1,367.75 2. What are the PVs of the streams at 0 percent compounded annually?

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Evaluating Return and Cash Flow Streams 10 [300 / (1 + .05)^¹] + [400 / (1 + .05)^²] + [400 / (1 + .05)^³] + [400 / (1 + .05)^⁴] + [100 / (1 + .05)^ ]⁵ [300 / (1.05)^¹] + [400 / (1.05)^²] + [400 / (1.05)^³] + [400 / (1.05)^⁴] + [100 / (1.05)^⁵ 300 / 1.05 + (400 / 1.1025) + 400 / 1.1576 + (400 / .1.2155) + 100 / 1.2762 285.714 + 362.811 + 345.542 + 329.082 + 78.357 = $1,401.51 0 1 2 3 4 5 Stream A $0 $100 $400 $400 $400 $300 Stream B $0 $300 $400 $400 $400 $100

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Quiz Instructions Question 1 1 pts A pension fund manager is considering three assets. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill yielding 0.06. Info of the risky funds is as follows: Expected ret. std. dev. Stock fund 0.22 0.27 Bond fund 0.12 0.14 The correlation between the fund returns is 0.5. What is the expected return of the optimal risky portfolio? Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

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A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows: Expected Return. Stock fund (5) Bond fund (B) The correlation between the fund returns is 0.10. 19% 14 Reg A1 Standard Deviation Required: a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds? a-2. What are the expected value and standard deviation of the minimum-variance portfolio rate of return? 31% 23 Complete this question by entering your answers in the tabs below. Reg A2 What are the expected value and standard deviation of the minimum-variance portfolio rate of return? Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.

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