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✨ Highlighted Calculation Practice

Midterm 2 Calculation Guide

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.

Quick setup tips
  1. Write the formula first.
  2. Label every variable before punching numbers.
  3. Check whether rates are annual or semiannual.
  4. For Chapter 8, check whether you need D₀ or D₁.

Chapter 6 Risk & Return • 5 sample calculations

Focus on the setup first, then the numbers. These are the most exam-like calculation patterns.

What usually gets calculated

HPR, expected return, portfolio expected return, CAPM required return, portfolio beta, and portfolio required return.
Main trap: confusing beta with standard deviation, or forgetting that portfolio expected return and portfolio beta use weighted averages.
Q1. Holding period return HPR
Big picture + method + common trap

You buy a stock for $50. One year later it is worth $56 and it paid a $2 dividend. Find the holding period return.

  1. Ending value = 56
  2. Beginning value = 50
  3. Cash flow = 2
  4. HPR = (56 − 50 + 2) / 50
Answer
HPR = 8 / 50 = 0.16 = 16%

Advice: include both price change and dividend.

Excel
=(56-50+2)/50
Q2. Expected return from states E(R)
Big picture + method + common trap

A 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.

  1. E(R)=ΣpR
  2. Multiply each return by its probability.
  3. Add the weighted returns.
Answer
E(R)=0.20(-8%)+0.50(12%)+0.30(24%)
= -1.6% + 6.0% + 7.2% = 11.6%
Excel
=0.2*(-8%)+0.5*12%+0.3*24%
Calculator
Open return calculator
Q3. Portfolio expected return Portfolio
Big picture + method + common trap

You invest 40% in Stock A with expected return 10% and 60% in Stock B with expected return 16%. Find portfolio expected return.

  1. E(Rp)=wA E(RA)+wB E(RB)
Answer
E(Rp)=0.4(10%)+0.6(16%)=13.6%
Excel
=0.4*10%+0.6*16%
Calculator
Open 2-stock portfolio calculator
Q4. CAPM required return CAPM
Big picture + method + common trap

The risk-free rate is 4%, market return is 11%, and a stock’s beta is 1.3. Find required return.

  1. r = rRF + β(rM − rRF)
  2. First find the market risk premium.
Answer
r = 4% + 1.3(11%−4%) = 4% + 1.3(7%) = 13.1%
Excel
=4%+1.3*(11%-4%)
Calculator
Open CAPM calculator
Q5. Two-stock portfolio beta and required return Portfolio Beta
Big picture + method + common trap

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.

  1. Find portfolio beta: βp = wAβA + wBβB
  2. Then use CAPM: rP = rRF + βP(rM − rRF)
Answer
βp = 0.35(0.80) + 0.65(1.40) = 0.28 + 0.91 = 1.19
rP = 4% + 1.19(10%−4%) = 4% + 1.19(6%) = 11.14%
Excel
=0.35*0.8+0.65*1.4
=4%+(1.19*(10%-4%))
Calculator
Open CAPM calculator

Chapter 7 Bond Pricing • 7 sample calculations

Excel-only path for Chapter 7: use PV, RATE, and simple formulas.

What usually gets calculated

Coupon payment, bond price, YTM, current yield, zero-coupon bond price, semiannual pricing, premium/discount interpretation.
Main trap: forgetting the semiannual conversion or mixing up coupon rate and YTM.
Q7. Annual coupon payment Coupon
Big picture + method + common trap

A bond has par value $1,000 and coupon rate 8%. What is the annual coupon payment?

  1. Use par value × coupon rate.
  2. Keep it simple in Excel.
Excel setup
=1000*8%
Answer
$80
Calculator
Open bond calculator
Q8. Price of an annual coupon bond Price
Big picture + method + common trap

A 10-year bond has par value $1,000, coupon rate 7%, and YTM 9%. Coupons are annual. Find price.

  1. Coupon = 1000×7% = 70
  2. Use Excel PV with rate = 9%, nper = 10, pmt = 70, fv = 1000.
  3. Multiply by -1 to show price as positive.
Excel setup
=PV(9%,10,70,1000)*-1
Answer
$871.65
Calculator
Open bond calculator
Q9. Price of a semiannual coupon bond Semiannual
Big picture + method + common trap

A 12-year bond has par value $1,000, coupon rate 6%, and YTM 8%, with semiannual coupons. Find price.

  1. Semiannual coupon = 1000×6%/2 = 30
  2. Periodic rate = 8%/2 = 4%
  3. Number of periods = 12×2 = 24
Excel setup
=PV(8%/2,12*2,1000*6%/2,1000)*-1
Answer
$847.53
Calculator
Open bond calculator
Q10. Yield to maturity from price YTM
Big picture + method + common trap

A bond sells for $950. It has par value $1,000, 8 years to maturity, and annual coupon rate 6%. Find YTM.

  1. Coupon payment = 1000×6% = 60
  2. Use Excel RATE with nper = 8, pmt = 60, pv = -950, fv = 1000.
Excel setup
=RATE(8,60,-950,1000)
Answer
6.83%
Calculator
Open bond calculator
Q11. Current yield Current Yield
Big picture + method + common trap

A bond pays an annual coupon of $90 and currently sells for $1,050. Find current yield.

  1. Current yield = annual coupon ÷ current price.
  2. Use one simple Excel formula.
Excel setup
=90/1050
Answer
8.57%
Calculator
Open bond calculator
Q12. Zero-coupon bond price Zero
Big picture + method + common trap

A zero-coupon bond has face value $1,000, 15 years to maturity, and YTM 5%. Find price.

  1. There are no coupon payments.
  2. Discount the face value back 15 years.
Excel setup
=1000/(1+5%)^15
Answer
$480.99
Calculator
Open bond calculator
Q13. Premium / discount / par check Interpret
Big picture + method + common trap

A bond’s coupon rate is 9% and its YTM is 7%. Should price be above, below, or equal to par?

  1. If coupon rate > YTM, bond price is above par.
  2. If coupon rate < YTM, bond price is below par.
  3. If coupon rate = YTM, bond price is at par.
Excel-style note
9% > 7% → premium bond
Answer
Above par
Calculator
Open bond calculator

Chapter 8 Stock Valuation • 7 sample calculations

Watch D₀ versus D₁ carefully. Most Chapter 8 mistakes happen before the formula even starts.

What usually gets calculated

Find D₁, price from Gordon, required return from Gordon, preferred stock value, dividend yield, capital gains yield, and simple two-stage stock price.
Main trap: using D₀ directly in the Gordon formula instead of first finding D₁.
Q14. Find next dividend D₁ D₁
Big picture + method + common trap

A stock just paid a dividend of $2.40. Dividends grow at 5%. Find next year’s dividend.

Answer
D₁ = D₀(1+g) = 2.40(1.05) = $2.52
Calculator
Open dividend calculator
Q15. Price using Gordon model P₀
Big picture + method + common trap

A stock just paid D₀ = $3.00. Dividends grow at 4% forever. Required return is 10%. Find today’s price.

  1. Find D₁ = 3.00(1.04)=3.12
  2. Use P₀ = D₁/(r-g)
Answer
P₀ = 3.12 / (0.10−0.04) = $52.00
Excel
=(3*(1+4%))/(10%-4%)
Calculator
Open dividend calculator
Q16. Required return from price r
Big picture + method + common trap

A stock sells for $40. Next year’s dividend is expected to be $2.20, and growth is 3.5%. Find required return.

Answer
r = D₁/P₀ + g = 2.20/40 + 3.5% = 5.5% + 3.5% = 9.0%
Calculator
Open dividend calculator
Q17. Dividend yield and capital gains yield Yield split
Big picture + method + common trap

A stock has D₁ = $1.80, P₀ = $30, and growth g = 4%. Find dividend yield, capital gains yield, and total expected return.

Answer
Dividend yield = 1.80/30 = 6%
Capital gains yield = g = 4%
Total expected return = 10%
Calculator
Open dividend calculator
Q18. Price one year from now P₁
Big picture + method + common trap

A stock has D₀ = $2.00, growth 6%, and required return 11%. Find P₁.

  1. Find D₁=2.12 and D₂=2.2472.
  2. P₁ = D₂/(r-g)
Answer
D₁ = 2(1.06)=2.12
D₂ = 2.12(1.06)=2.2472
P₁ = 2.2472 / (0.11−0.06) = $44.94
Calculator
Open dividend calculator
Q19 - Extra Credit Question. Simple two-stage stock valuation Two-stage
Big picture + method + common trap

A 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.

  1. D₁ = 1.50(1.12)=1.6800
  2. D₂ = 1.6800(1.12)=1.8816
  3. D₃ = 1.8816(1.05)=1.97568
  4. Terminal value at year 2: P₂ = D₃/(r-g)
  5. Discount D₁, D₂, and P₂ back to time 0.
Answer
P₂ = 1.97568/(0.11−0.05)=32.928
P₀ = 1.6800/1.11 + 1.8816/(1.11)^2 + 32.928/(1.11)^2
≈ 1.5135 + 1.5276 + 26.7337 = $29.77
Advice
Do not apply the Gordon model until the stock reaches the stable-growth stage.
Calculator
Open dividend calculator