Finance Ch 6 Quiz

Westco Company issued 14-year bonds one year ago at a coupon rate of 7.4 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 5.4 percent, what is the current price of the bond in dollars?

$1,185.10 To find the price of this bond, we need to realize that the maturity of the bond is 13 years. The bond was issued one year ago, with 14 years to maturity, so there are 13 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P = $37.00(PVIFA2.70%,26) + $1,000(PVIF2.70%,26) P = $1,185.10

Union Local School District has bonds outstanding with a coupon rate of 3.5 percent paid semiannually and 13 years to maturity. The yield to maturity on these bonds is 2.5 percent and the bonds have a par value of $10,000. What is the dollar price of the bonds?

$11,104.06 To find the price of this bond, we need to find the present value of the bond's cash flows. So, the price of the bond is: P = $175(PVIFA1.25%,26) + $10,000(PVIF1.25%,26) P = $11,104.06

You find a zero coupon bond with a par value of $10,000 and 14 years to maturity. The yield to maturity on this bond is 5.1 percent. Assume semiannual compounding periods. What is the price of the bond?

$4,940.85 To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P = $10,000(PVIF2.55%,28) P = $4,940.85

Yan Yan Corporation has a $5,000 par value bond outstanding with a coupon rate of 4.8 percent paid semiannually and 27 years to maturity. The yield to maturity on this bond is 4.8 percent. What is the dollar price of the bond?

$5,000.00 To find the price of this bond, we need to find the present value of the bond's cash flows. So, the price of the bond is: P = $120(PVIFA2.40%,54) + $5,000(PVIF2.40%,54) P = $5,000.00

Draiman Corporation has bonds on the market with 19 years to maturity, a YTM of 11.1 percent, a par value of $1,000, and a current price of $937. The bonds make semiannual payments. What must the coupon rate be on the bonds?

10.30% Here, we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $937 = C(PVIFA5.55%,38) + $1,000(PVIF5.55%,38) Solving for the coupon payment, we get: C = $51.49 Since this is the semiannual payment, the annual coupon payment is: 2 × $51.49 = $102.98 And the coupon rate is the coupon payment divided by par value, so: Coupon rate = $102.98/$1,000 Coupon rate = .1030, or 10.30%

Say you own an asset that had a total return last year of 18 percent. Assume the inflation rate last year was 4.9 percent. What was your real return?

12.49% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) r = [(1 + .18)/(1 + .049)] − 1 r = .1249, or 12.49%

Setrakian Industries needs to raise $48.5 million to fund a new project. The company will sell bonds that have a coupon rate of 5.56 percent paid semiannually and that mature in 10 years. The bonds will be sold at an initial YTM of 6.13 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds?

25,317 bonds PV = $55.60{1 − [1/(1 + .0613/2)20]}/(.0613/2) + $2,000/(1 + .0613/2)20 PV = $1,915.71 Bonds to sell = $48,500,000/$1,915.71 = 25,317

An investment offers a total return of 12 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 8.3 percent. What does Janice believe the inflation rate will be over the next year?

3.42% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) h = [(1 + .12)/(1 + .083)] − 1 h = .0342, or 3.42%

Suppose the real rate is 3.85 percent and the inflation rate is 1.3 percent. What rate would you expect to see on a Treasury bill?

5.20% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) R = (1 + .0385)(1 + .013) − 1 R = .0520, or 5.20%

A Japanese company has a bond that sells for 103.813 percent of its ¥100,000 par value. The bond has a coupon rate of 6.5 percent paid annually and matures in 23 years. What is the yield to maturity of this bond?

6.22% Here, we need to find the YTM of a bond. The equation for the bond price is: P = ¥103,813 = ¥6,500(PVIFAR%,23) + ¥100,000(PVIFR%,23) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 6.18%

You find the following corporate bond quotes. To calculate the number of years until maturity, assume that it is currently January 15, 2022. The bonds have a par value of $2,000 and semiannual coupons.

6.53% Here, we need to find the coupon rate of the bond. The dollar price of the bond is: Dollar price = (94.835/100) × $2,000 Dollar price = $1,896.70 Now, what we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $1,896.70 = C(PVIFA3.52%,36) + $2,000(PVIF3.52%,36) Solving for the coupon payment, we get: C = $65.29 Since this is the semiannual payment, the annual coupon payment is: 2 × $65.29 = $130.59 And the coupon rate is the coupon rate divided by par value, so: Coupon rate = $130.59/$2,000 Coupon rate = .0653, or 6.53%

A bond with a current yield of 6.85 percent is quoted at 96.993. What is the coupon rate of the bond?

6.64% Annual coupon = .0685 × ($96.993 × 10) = $66.44 Coupon rate = $66.44/$1,000 = .0664, or 6.64%

Uliana Company wants to issue new 18-year bonds for some much-needed expansion projects. The company currently has 8.9 percent coupon bonds on the market that sell for $1,129, make semiannual payments, have a par value of $1,000, and mature in 18 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

7.58% P = $1,129 = $44.50(PVIFAR%,36) + $1,000(PVIFR%,36) Using a spreadsheet, financial calculator, or trial and error, we find: R = 3.788% This is the semiannual interest rate, so the YTM is: YTM = 2 × 3.788% YTM = 7.58%

Nikita Enterprises has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and selling for $958. At this price, the bonds yield 8.9 percent. What must the coupon rate be on the bonds?

8.36% Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $958 = C(PVIFA8.9%,14) + $1,000(PVIF8.9%,14) Solving for the coupon payment, we get: C = $83.64 The coupon payment is the coupon rate times par value. Using this relationship, we get: Coupon rate = $83.64/$1,000 Coupon rate = .0836, or 8.36%

If Treasury bills are currently paying 6.15 percent and the inflation rate is 2 percent, what is the approximate and the exact real rate of interest?

Approx 4.15% Exact 4.07% The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h), is: R ≈ r + h Approximate r = .0615 − .020 Approximate r = .0415, or 4.15% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) (1 + .0615) = (1 + r)(1 + .020) Exact r = [(1 + .0615)/(1 + .020)] − 1 Exact r = .0407, or 4.07%

Williams Software has 7.8 percent coupon bonds on the market with 25 years to maturity. The bonds make semiannual payments and currently sell for 108.75 percent of par. a) What is the current yield on the bonds? b) What is the YTM? c) What is the effective annual yield?

a. 7.17% b. 7.04% c. 7.16% a. The current yield is: Current yield = Annual coupon payment/Price Current yield = $78/$1,087.50 Current yield = .0717, or 7.17% b. The bond price equation for this bond is: P0 = $1,087.50 = $39.00(PVIFAR%,50) + $1,000(PVIFR%,50) Using a spreadsheet, financial calculator, or trial and error we find: R = 3.525% This is the semiannual interest rate, so the YTM is: YTM = 2 × 3.525% YTM = 7.05% c. The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + .03525)2 − 1 Effective annual yield = .0717, or 7.17%

Suppose the following bond quote for IOU Corporation appears in the financial page of today's newspaper. Assume the bond has a face value of $2,000, and the current date is April 19, 2022. Company (Ticker)CouponMaturityLast PriceLast YieldEstimated Volume (000s)IOU (IOU)7.80April 19, 204393.064??111 a) What is the yield to maturity of the bond? b) What is the current yield?

a. 8.51% b. 8.38% a. The bond has 21 years to maturity, so the bond price equation is: P = $1,861.28 = $78.00(PVIFAR%,42) + $2,000(PVIFR%,42) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.257% This is the semiannual interest rate, so the YTM is: YTM = 2 × 4.257% YTM = 8.51% b. The current yield is the annual coupon payment divided by the bond price, so: Current yield = $156.00/$1,861.28 Current yield = .0838, or 8.38%

Bond J has a coupon rate of 4.1 percent. Bond K has a coupon rate of 14.1 percent. Both bonds have nine years to maturity, a par value of $1,000, and a YTM of 9.2 percent, and both make semiannual payments. a) If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds? b) If interest rates suddenly fall by 3 percent instead, what is the percentage change in the price of these bonds?

a. Bond P: -18.43% & Bond D: -14.93% b. Bond P: 23.75% & Bond D: 18.77% a. Initially, at a YTM of 9.2 percent, the prices of the two bonds are: PJ = $20.50(PVIFA4.6%,18) + $1,000(PVIF4.6%,18) = $692.38 PK = $70.50(PVIFA4.6%,18) + $1,000(PVIF4.6%,18) = $1,295.56 If the YTM rises from 9.2 percent to 12.2 percent: PJ = $20.50(PVIFA6.1%,18) + $1,000(PVIF6.1%,18) = $564.76 PK = $70.50(PVIFA6.1%,18) + $1,000(PVIF6.1%,18) = $1,102.09 The percentage change in price is calculated as: Percentage change in price = (New price − Original price)/Original price ΔPJ% = ($564.76 − 692.38)/$692.38 = −.1843, or −18.43% ΔPK% = ($1,102.09 − 1,295.56)/$1,295.56 = −.1493, or −14.93% b. If the YTM declines from 9.2 percent to 6.2 percent: PJ = $20.50(PVIFA3.1%,18) + $1,000(PVIF3.1%,18) = $856.80 PK = $70.50(PVIFA3.1%,18) + $1,000(PVIF3.1%,18) = $1,538.70 ΔPJ% = ($856.80 − 692.38)/$692.38 = .2375, or 23.75% ΔPK% = ($1,538.70 − 1,295.56)/$1,295.56 = .1877, or 18.77%

Bond P is a premium bond with a coupon rate of 9 percent. Bond D is a discount bond with a coupon rate of 5 percent. Both bonds make annual payments, a YTM of 7 percent, a par value of $1,000, and have five years to maturity. a) What is the current yield for Bond P? For Bond D? b)If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D?

a. Bond P: 8.32% & Bond D: 5.45% b. Bond P: -1.31% & Bond D: 1.56% To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is: P: P0 = $90(PVIFA7%,5) + $1,000(PVIF7%,5) P0 = $1,082.00 P1 = $90(PVIFA7%,4) + $1,000(PVIF7%,4) P1 = $1,067.74 The current yield is: Current yield = $90/$1,082.00 Current yield = .0832, or 8.32% The capital gains yield is: Capital gains yield = (New price − Original price)/Original price Capital gains yield = ($1,067.74 − 1,082.00)/$1,082.00 Capital gains yield = −.0132, or −1.32% The current price of Bond D and the price of Bond D in one year is: D: P0 = $50(PVIFA7%,5) + $1,000(PVIF7%,5) P0 = $918.00 P1 = $50(PVIFA7%,4) + $1,000(PVIF7%,4) P1 = $932.26 The current yield is: Current yield = $50/$918.00 Current yield = .0545, or 5.45% The capital gains yield is: Capital gains yield = ($932.26 − 918.00)/$918.00 Capital gains yield = .0155, or 1.55%