FRL 300 Homework 5 (Chapter 7)
8.value: 10.00 points An investment offers a total return of 17 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 13 percent. What does Janice believe the inflation rate will be over the next year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Inflation rate %
FISHER EFFECT --nominal rate is like interest rate or rate of return (1+R)=(1+r)(1+h) (1+ nominal rate)=(1+ real rate )(1+ *expected inflation rate*) inflation rate = (1+nominal)(1+real)-1 = (1.17)(1.13) - 1 = 0.03540 = *3.54%* is the inflation rate
7.value: 10.00 points Treasury bills are currently paying 6 percent and the inflation rate is 3.3 percent. What is the approximate real rate of interest? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Approximate real rate % What is the exact real rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Exact real rate %
FISHER EFFECT --nominal rate is like interest rate or rate of return (1+R)=(1+r)(1+h) (1+ nominal rate)=(1+ real rate )(1+ expected inflation rate) a. approximate real rate = 6-3.3 = *2.7%* b. exact real rate (1+ nominal rate)=(1+ *real rate* )(1+ expected inflation rate) (1+ *real rate* )=(1+ nominal rate) / (1+ expected inflation rate) real rate = (1.06)(1.033) - 1 = 0.02614 = *2.61%*
9.value: 10.00 points Say you own an asset that had a total return last year of 11.2 percent. If the inflation rate last year was 5.9 percent, what was your real return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Real return %
FISHER EFFECT --nominal rate is like interest rate or rate of return (1+R)=(1+r)(1+h) (1+ nominal rate)=(1+ real rate )(1+ expected inflation rate) (1+ *real rate* )=(1+ nominal rate) / (1+ expected inflation rate) real = (1.112) / (1.059) - 1 = 0.05005 = *5.00%* is the real rate
10.value: 10.00 points Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 10 percent, has a YTM of 8 percent, and has 20 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 8 percent, has a YTM of 10 percent, and also has 20 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of Bond X $ Price of Bond Y $ If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In 10 years? In 15 years? In 19 years? In 20 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.) Price of bond Bond X Bond Y One year $ 10 years $ 15 years $ 19 years $ 20 years $
a. price of bond x $ fv = 1,000 n = 20*2 = 40 i = 8/2 = 4 pmt = (1,000*0.1)/2 = 50 cpt, *pv bond x = 1,197.92* price of box y $ i = 10/2 = 5 pmt = (1,000*0.08)/2 = 40 cpt, *pv bond y= 828.71* b. BOND X: 1 yr => n = (20-1) x 2 = 38; cpt, *pv = 1,193.68* 10 yrs => n = (20-10) x 2 = 20; cpt, *pv = 1,1,35.90* 15 yrs => n = (20-15) x 2 = 10; cpt, *pv = 1,081.11* 19 yrs => n = (20-19) x 2 = 2; cpt, *pv = 1,018.86* 20 yrs => n = 0; cpt, *pv = 1,000* BOND Y: (change i = 5 & pmt = 40... then repeat n's from above^) 1 yr => n = 38; cpt, *pv = 831.32* 10 yrs => n = 20; cpt, *pv = 875.38* 15 yrs => n = 10; cpt, *pv = 922.78* 19 yrs => n = 2; cpt, *pv = 981.41* 20 yrs => n = 0; cpt, *pv = 1,000*
2.value: 10.00 points A Japanese company has a bond outstanding that sells for 90 percent of its ¥100,000 par value. The bond has a coupon rate of 4.9 percent paid annually and matures in 20 years. What is the yield to maturity of this bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Yield to maturity %
fv=100,000 pv=100,000*.9=> -90,000 pmt=100,000*.049 = 4,900 n=20 cpt, *i=5.75%*
1.value: 10.00 points Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 25 years to maturity, and a coupon rate of 7.9 percent paid annually. If the yield to maturity is 9 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price €
fv=1000 n=25 pmt= 1000*.079 = 79 i=9 cpt, *pv=891.95*
6.value: 10.00 points Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 18 years to maturity. The yield to maturity on this bond is 4.7 percent. What is the price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price $
n = 18*2 = 36 i = 4.7/2 = 2.35 pmt = 2,000*0.022 = 44 fv = 2,000 cpt, *pv = 1,927.66*
5.value: 10.00 points DMA Corporation has bonds on the market with 18.5 years to maturity, a YTM of 7.9 percent, and a current price of $1,067. The bonds make semiannual payments and have a par value of $1,000. What must the coupon rate be on these bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Coupon rate %
n=18.5*2 = 37 i=7.9/2 = 3.95 pv= -1,067 fv=1,000 cpt, *pmt=42.97539* ^ SEMIANNUAL PAYMENT IN $ To calculate coupon % per year: (*42.975398* x 2) / 1,000 => *8.60%*
3.value: 10.00 points Essary Enterprises has bonds on the market making annual payments, with nine years to maturity, a par value of $1,000, and selling for $966. At this price, the bonds yield 6.8 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Coupon rate %
n=9 fv=1,000 pv= -966 i=6.8 cpt, pmt=62.82577 62.8577/1,000 = *6.28%*
4.value: 10.00 points Heginbotham Corp. issued 10-year bonds two years ago at a coupon rate of 8.4 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) YTM %
pv = 1,000*1.05 => -1,050 fv = 1000 n = # of periods = 2(10-2) = 16 pmt = 1,000*(0.084/2) = 42 cpt, *i=3.77790* ^ THIS IS THE SEMIANNUAL PAYMENT % *3.77790* x 2 => *7.56%*