Week 5 - FIN 3113 OSU Ch. 6-7

Annuity

A stream of constant cash flows that lasts for a fixed number of periods

Staind, Inc., has 8 percent coupon bonds on the market that have 6 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 10 percent, what is the current bond price?

Calculate on calculator for PV coupon rate= 8% maturity= 6 YTM= 10% FV= $1,000

Caan Corporation will pay a $2.90 per share dividend next year. The company pledges to increase its dividend by 4 percent per year indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company's stock today?

Po= D1/(R-g) D1= $2.90 R= 11% g= 4%

Metroplex Corporation will pay a $5.90 per share dividend next year. The company pledges to increase its dividend by 5.40 percent per year indefinitely. If you require an 9.80 percent return on your investment, how much will you pay for the company's stock today?

Po= D1/(R-g) D1= 5.90 R= 9.8% g= 5.4% Po= ?

Types of Annuities

- Ordinary Annuities Have Cash Flows at the END of Each Period -An Annuity Due Has Cash Flows at the BEGINNING of Each Period -Value Annuity Due = Value Ordinary Annuity * (1+r)

Far Side Corporation is expected to pay the following dividends over the next four years: $8, $7, $5, and $2. Afterward, the company pledges to maintain a constant 7 percent growth rate in dividends forever. If the required return on the stock is 16 percent, what is the current share price?

D1= 8 D2= 7 D3= 5 D4=2 g= 7% R= 16% Po= Dnx(1+g)/(R-g) P4= 2x(1+0.07)/(0.16-0.07)= $23.78 Po= D1/(1+R)^1 + D2/(1+R)^2 + D3/(1+R)^3 + D1/(1+R)^4 + P4/(1+R)^4 Po= 8/(1.16)^1 + 7/(1.16)^2 + 5/(1.16)^3 + 2/(1.16)^4 + 23.78/(1.16)^4

A Japanese company has a bond outstanding that sells for 86 percent of its ¥100,000 par value. The bond has a coupon rate of 4.5 percent paid annually and matures in 16 years. What is the yield to maturity of this bond?

FV= $100,000 PV= $86,000 maturity (N)= 16 coupon rate= 4.5% PMT= 86,000x4.5%= $3,870 YTM= ?

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 7 years because the firm needs to plow back its earnings to fuel growth. The company will pay a $10 per share dividend in 8 years and will increase the dividend by 6 percent per year thereafter. If the required return on this stock is 10 percent, what is the current share price?

Po= D8 x (1+g)/(R-g) P8= 10 x (1.06)/(0.10-0.06)= 265 Po= D8/(1+R)^8 + P8/(1+R)^8 Po= 10/(1.10)^8 + 265/(1.10)^8

Suppose the real rate is 5.5 percent and the inflation rate is 3 percent. What rate would you expect to see on a Treasury bill?

R= (1+r)x(1+h)-1 r= 5.5% h= 3% R=?

Suppose the real rate is 6.5 percent and the inflation rate is 1.8 percent. What rate would you expect to see on a Treasury bill?

R= (1+r)x(1+h)-1 r= 6.5% h= 1.8% R=?

The next dividend payment by Halestorm, Inc., will be $1.44 per share. The dividends are anticipated to maintain a growth rate of 6 percent forever. If the stock currently sells for $26 per share, what is the required return?

R= (D1/Po)+g D1= 1.44 Po= $26 g= 6%

The next dividend payment by Hot Wings, Inc., will be $2.05 per share. The dividends are anticipated to maintain a 3 percent growth rate forever. If the stock currently sells for $52 per share, what is the required return?

R= (D1/Po)+g D1= 2.05 g= 3% Po= $52 R=?

An investment offers a 10.5 percent total return over the coming year. Bill Bernanke thinks the total real return on this investment will be only 4.0 percent. What does Bill believe the inflation rate will be over the next year?

h= (1+R)/(1+r)-1 R= 10.5% r= 4% h=?

Heginbotham Corp. issued 20-year bonds two years ago at a coupon rate of 7.7 percent. The bonds make semiannual payments. If these bonds currently sell for 107 percent of par value, what is the YTM?

maturity= 18/2= 36 FV= $1,000 coupon rate= 7.7%/2= 3.85% PV= $1,000 x 107%= $1,070 PMT= $1,000 x 0.077= $77/2= $38.50 YTM semi annually=? x 2 YTM annually = ?

Grohl Co. issued 8-year bonds a year ago at a coupon rate of 6 percent. The bonds make semiannual payments. If the YTM on these bonds is 10 percent, what is the current bond price?

maturity= 7x2= 14 years YTM= 10%/2= 5% coupon rate= 6%/2= 3% PMT= 1,000x3%= $30 PV= ?

Say you own an asset that had a total return last year of 17.5 percent. If the inflation rate last year was 4.5 percent, what was your real return?

r= (1+R)/(1+h)-1 R= 17.5% h= 4.5% r=?