Chapters 6–8 only. This page gives 19 sample calculation problems across risk and return, bond pricing, and stock valuation. Each one shows the main setup, the formula path, and the key idea to notice.
Chapter 6 Risk & Return • 5 sample calculations
You buy a stock for $50. One year later it is worth $56 and it paid a $2 dividend. Find the holding period return.
HPR = (56 − 50 + 2) / 50HPR = 8 / 50 = 0.16 = 16%Advice: include both price change and dividend.
Excel=(56-50+2)/50A stock has these possible returns: recession -8% with probability 0.20, normal 12% with probability 0.50, boom 24% with probability 0.30. Find expected return.
E(R)=ΣpRE(R)=0.20(-8%)+0.50(12%)+0.30(24%)= -1.6% + 6.0% + 7.2% = 11.6%=0.2*(-8%)+0.5*12%+0.3*24%You invest 40% in Stock A with expected return 10% and 60% in Stock B with expected return 16%. Find portfolio expected return.
E(Rp)=wA E(RA)+wB E(RB)The risk-free rate is 4%, market return is 11%, and a stock’s beta is 1.3. Find required return.
r = rRF + β(rM − rRF)r = 4% + 1.3(11%−4%) = 4% + 1.3(7%) = 13.1%=4%+1.3*(11%-4%)You invest 35% in Stock A with beta 0.80 and 65% in Stock B with beta 1.40. The risk-free rate is 4% and the market return is 10%. Find the portfolio beta and the portfolio required return.
βp = wAβA + wBβBrP = rRF + βP(rM − rRF)βp = 0.35(0.80) + 0.65(1.40) = 0.28 + 0.91 = 1.19rP = 4% + 1.19(10%−4%) = 4% + 1.19(6%) = 11.14%=0.35*0.8+0.65*1.4=4%+(1.19*(10%-4%))Chapter 7 Bond Pricing • 7 sample calculations
A bond has par value $1,000 and coupon rate 8%. What is the annual coupon payment?
A 10-year bond has par value $1,000, coupon rate 7%, and YTM 9%. Coupons are annual. Find price.
1000×7% = 70-1 to show price as positive.A 12-year bond has par value $1,000, coupon rate 6%, and YTM 8%, with semiannual coupons. Find price.
1000×6%/2 = 308%/2 = 4%12×2 = 24A bond sells for $950. It has par value $1,000, 8 years to maturity, and annual coupon rate 6%. Find YTM.
1000×6% = 60A bond pays an annual coupon of $90 and currently sells for $1,050. Find current yield.
A zero-coupon bond has face value $1,000, 15 years to maturity, and YTM 5%. Find price.
A bond’s coupon rate is 9% and its YTM is 7%. Should price be above, below, or equal to par?
Chapter 8 Stock Valuation • 7 sample calculations
D₁, price from Gordon, required return from Gordon, preferred stock value, dividend yield, capital gains yield, and simple two-stage stock price.D₀ directly in the Gordon formula instead of first finding D₁.A stock just paid a dividend of $2.40. Dividends grow at 5%. Find next year’s dividend.
A stock just paid D₀ = $3.00. Dividends grow at 4% forever. Required return is 10%. Find today’s price.
D₁ = 3.00(1.04)=3.12P₀ = D₁/(r-g)A stock sells for $40. Next year’s dividend is expected to be $2.20, and growth is 3.5%. Find required return.
A stock has D₁ = $1.80, P₀ = $30, and growth g = 4%. Find dividend yield, capital gains yield, and total expected return.
Dividend yield = 1.80/30 = 6%Capital gains yield = g = 4%Total expected return = 10%A stock has D₀ = $2.00, growth 6%, and required return 11%. Find P₁.
D₁=2.12 and D₂=2.2472.P₁ = D₂/(r-g)D₁ = 2(1.06)=2.12D₂ = 2.12(1.06)=2.2472P₁ = 2.2472 / (0.11−0.06) = $44.94A stock just paid D₀ = $1.50. Dividends will grow at 12% for the next 2 years, then at 5% forever. Required return is 11%. Find price today.
D₁ = 1.50(1.12)=1.6800D₂ = 1.6800(1.12)=1.8816D₃ = 1.8816(1.05)=1.97568P₂ = D₃/(r-g)D₁, D₂, and P₂ back to time 0.P₂ = 1.97568/(0.11−0.05)=32.928P₀ = 1.6800/1.11 + 1.8816/(1.11)^2 + 32.928/(1.11)^2≈ 1.5135 + 1.5276 + 26.7337 = $29.77