Fina6000 Finance|Interest Rates Assessment Answer
You have $6 150 to deposit. Regency Bank offers 12 percent per year compounded monthly while King Bank offers 12 percent but will only compound annually. How much will your investment be worth in 20 years at each bank? Effective interest rate for Regency Bank is EAR = [ 1 + r/m]^m -1 = [1 + 0.12/12]^12 -1 = 12.6825% EAR for King Bank is 12% Future Value of investment at Regency Bank …..FVn = PV x (1 +EAR)^ n = 6150 x (1.126825)^20 = 66 989.17 Future Value of investment at King Bank = 6150 x (1.12)^20 = 59 324.70 Question 2 You have decided that you want to be a millionaire when you retire in 45 years. If you can earn an annual return of 11 percent, how much do you have to invest today? What if you can earn 5.5 percent per annum? Question requires you to calculate the Present value (PV) At 11% per annum FVn = PV x (1+ r)^n Millionaire means having a $1 000 000. PV x (1.11)^45 = 1000 000 Thus PV = 1000 000/(1.11^45) = $9 129.90 At 5.5% per annum FVn = PV x ( Millionaire means having a $1 000 000. PV x (1.055)^45 = 1000 000 Thus PV = 1000 000/(1.055^45) = $89 875.09 Question 3 Beginning three months from now you want to be able to withdraw $2 500 each quarter from your bank account to cover college expenses over the next four years. If the account pays 0.38 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years? Better to draw a timeline to see the cashflows properly. Question requires to determine PV of an ordinary annuity PV = C/r x [1 – 1/(1 + r )^n] = 2500/0.0038 x [ 1 – 1/(1.0038^16] = 2500 x 15.49477355 = 38 736.93 Question 4 You have recently finished your MBA at Torrens University Australia. Naturally, you must purchase a new BMW immediately. The car costs about $42 000. The bank quotes an interest rate of 15% APR for a 72-month loan with a 10% down payment. What will your monthly payment be? What is the effective interest rate on the loan? Effective interest rate per month = APR/m = 15%/12 =1.25% Deposit on car = 0.10 x 42 000 = 4 200 Amount of loan = 42 000 – 4 200 = 37 800. Let C be monthly payment Loan value = PV of monthly repayments at 1.25% 37 800 = C/r x [1 – 1/(1 + r )^n] = C/0.0125 x [1 – 1/(1.0125^72)] = C x 47.29247431 Therefore C = 799.28 Monthly repayment is $799.28. Effective Annual Rate (EAR) = (1.0125)^12 -1 = 16.08% Question 5 Lycan Inc. has 7 percent coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments and have a par value of $1 000. If the yield to maturity (YTM) on these bonds is 8.4 percent per annum, what is the current bond price? Amount of coupon (C) = 7% of face value = 0.07 x 1000 = 70 Value of bond = PV of Coupon payments + PV of Face Value = C/r x [1 – 1/(1+r)^n] + Face Value/(1+r)^n] = (70/0.084) x [1 - (1/(1.084^9)] + 1000/(1.084^9) = 70 x 6.144301788 + 1000 x 0.48387865 = 430.1011252 + 483.8786498 = 913.98 Question 6 Yan Yan Corp. has a $2 000 par value bond outstanding with a coupon rate of 4.9 percent paid semi-annually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the price of the bond? Working in half years: Coupon rate per period =4.9%/2 = 2.45% Amount of coupon = 0.0245 x 2 000 = 49 Yield per period = 3.8%/2 = 1.9%. N= 13 x 2 = 26 Value of bond = PV of Coupon payments + PV of Face Value = (49/0.019 x [1 - (1/(1.019^26)] + 2000/(1.019^26) =49 x 20.36762308 + 2000 x 0.613015161 = 998.0135 + 1226.0303 = 2224.04 Question 7 Discuss the concept of interest rate risk with regards to an investment in bonds. In your opinion, is a bond investor free from exposure to interest rate risk? When market interest rates increase bond investors demand higher yields. However, the value of bonds decrease with high yields resulting in investors experience a capital loss. The opposite is true for a decrease in interest rates which results in bond values increasing, thus generating capital gains for the investors. The uncertainty surrounding the value of a bond due to changes in interest rates is termed price risk. Bond investors are also exposed to reinvestment risk. The coupon payments that they are entitled to receive from the bond are fixed in amount. However, the investors have uncertainty about the rate of return they could get when they reinvest the coupon payments. This is due to possibilities of market interest rates changing. A decrease in rates implies getting a lower return on reinvestment. An increase in market interest rates would mean they get a higher return. Combining the price risk plus the reinvestment risk is what makes the interest risk for a bond investor. Long-term bonds have more price risk than short-term bonds. Low coupon bonds have more price risk than high coupon bonds. Short-term bonds have more reinvestment rate risk than long-term bonds. High coupon bonds have more reinvestment risk than low coupon bonds. Question 8 One of the ways of determining the value of equity is the discounted cash flow (DCF) approach which takes a number of different forms. The Dividend valuation models belong to the DCF techniques. Discuss the Dividend valuation approach explaining three different forms of the approach providing assumptions made in each. Value of shares = PV of future cash flows generated by the shares. In the case of the Dividend Valuation model the cash flows are the dividends. The model takes different form depending on the nature of the growth in dividends. Assuming zero growth in dividends
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