Unit Exercise of chapter 7 and 8 PDF

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Unit exercise of the chapter 7 that highlighted cash flow calculation...

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Unit Exercise 7 Chapter 6

Problem 1 Present Value and Multiple Cash Flows [LO1] Seaborn Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at18 percent? At 24 percent? Discount rate = 10 PV = $950/1.10 + $1,040/1.102 +$1,130/1.103 + $1,075/1.104 = $3,348 Discount rate = 18 PV = $950/1.18 + $1040/1.182 +$1130/1.183 + $1075/1.184 = $2,794 Discount rate = 24 PV = $950/1.24 + $1040/1.242 +$1130/1.243 + $1075/1.244 = $2,489.74 Problem 4 Calculating Annuity Present Value [LO1] An investment offers $5,300 per year for 15 years, with the first payment occurring one year from now. If the required return is 7 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever? N = 15 + 1 years; I/Y = 7; PMT = $5,300 CPT PV = $ 48,271.94 N = 40 + 1years; I/Y = 7; PMT = $5,300 CPT PV = $ 70,658.06 N = 75+ 1 years; I/Y = 7; PMT= $5,300 CPT PV = $ 75,240.70 Forever PV = C / r PV = $5,300/0.07 = $75,714.29 Problem 22 Calculating EAR [LO4] Friendly’s Quick Loans, Inc., offers you “three for four or 1 knock on your door.” This means you get $3 today and repay $4 when you get your paycheck in one week (or else). What’s the effective annual return Friendly’s earns on this lending business? If you were brave enough to ask, what APR would Friendly’s say you were paying?

PV = FV/ (1+r) t 3 = 4 / (1+ r) 1 r = 4/3 – 1 = 33,33334 % Let find the APR APR = 33,33334% x 52 = 1,733%

A PR ù é E A R = ê1 + m úû ë

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EAR = [1 + 1.733/52]52 – 1 = 313,916 % EAR = 313,916 % Problem 29 Simple Interest versus Compound Interest [LO4] First Simple Bank pays 7 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years? The simple interest over the 10 years is 0.07(10) = 0.70 Since the first simple bank pays compound interest, the interest will be future value of a dollar. 0.07(10) = (1+r)10 – 1 1.7 = (1+r)10 r = (1.7)1/10 – 1 = 5.44% r = 5.44%

Chapter 7 Problem 2 Interpreting Bond Yields [LO2] Suppose you buy a 7 percent coupon, 20-year bond today when it’s first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why?

If the interest rate rises from 7% to 15%, the value of the bond will decrease. This happens because of the connection between the interest rate and the bond yield. When the interest rate rises, the price of the bond will fall and when the interest rate decreases, the bond price will suddenly increase. From the given problem above, the interest rate increases from 7 to 15 percent, therefore the value of the bond will decrease. Problem 5 Coupon Rates [LO2] Kiss the Sky Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,045. At this price, the bonds yield 7.5 percent. What must the coupon rate be on the bonds? Assuming FV = $1,000 N= 13 years; I/Y = 7.5% Pv = $1,045; FV = $1,000 CPT PMT = 80.54 Coupon rate = 80.54/1000 = 8.05% Problem 9 Calculating Real Rates of Return [LO4] If Treasury bills are currently paying 7 percent and the inflation rate is 3.8 percent, what is the approximate real rate of interest? The exact real rate? R=r+h r = R – h = 7 – 3.8 = 3.20% real rate of interest = 3.20% For the exact real rate (1 + R) = (1 + r)(1 + h) r = (1+R)/(1+h) – 1 r = [1.07/1.038] – 1 = 0.0308 r = 3.08%

Problem 20 Accrued Interest [LO2] You purchase a bond with an invoice price of $968. The bond has a coupon rate of 7.4 percent, and there are four months to the next semi-annual coupon date. What is the clean price of the bond? Accrued Interest = (74/2) x (2/6) = $12.33 Knowing that the coupon rate is 7.4%, therefore, the annual coupon is 1000 x 0.074 = $74

Clean price = dirty price – Accrued interest Clean price = $968 - $12.33 = $955.67 Clean price = $955.67 Problem 23 Using Bond Quotes [LO2] Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is April 15, 2009. What is the yield to maturity of the bond? What is the current yield? N = 14; PV = $1,089.60; PMT= 72; FV= $1,000; CPT I/Y = 6.22%

Current yield = Annual coupon / Price Current yield = 72/$1,089.60 = 0.0661 Current yield = 6,61%...