Question

Four years ago, Sam invested in Grath Oil. She bought three of its $1,000 par value bonds at a market price of 93.938 and with an annual coupon rate of 6.5%. She also bought 450 shares of Grath Oil stock at $44.11, which has paid an annual dividend of $3.10 for each of the last ten years. Today, Grath Oil bonds have a market rate of 98.866 and Grath Oil stock sells for $45.55 per share.

Answer 1

I’ll assume the quoted bond prices (93.938 and 98.866) are percent of par (so price = percent × $1,000), coupons/dividends are paid annually, and Sam still holds the securities today. Results below are rounded to 2 decimal places.

1) Bonds (3 bonds, $1,000 par, 6.5% coupon)
- Purchase price per bond = 93.938% × $1,000 = $939.38
- Total purchase cost = 3 × $939.38 = $2,818.14
- Annual coupon per bond = 6.5% × $1,000 = $65 → 3 bonds → $195/yr
- Coupons received over 4 years = 4 × $195 = $780.00
- Current price per bond = 98.866% × $1,000 = $988.66
- Current market value = 3 × $988.66 = $2,965.98
- Total dollar return = coupons + price change = $780 + ($2,965.98 − $2,818.14) = $927.84
- Total percentage return over 4 years = $927.84 / $2,818.14 = 32.92%
- Annualized return = (1 + 0.3292)^(1/4) − 1 ≈ 7.37% per year

2) Stock (450 shares)
- Purchase cost = 450 × $44.11 = $19,849.50
- Dividend per share = $3.10 → annual dividends = 450 × $3.10 = $1,395
- Dividends received over 4 years = 4 × $1,395 = $5,580.00
- Current market value = 450 × $45.55 = $20,497.50
- Total dollar return = dividends + price change = $5,580 + ($20,497.50 − $19,849.50) = $6,228.00
- Total percentage return over 4 years = $6,228 / $19,849.50 = 31.39%
- Annualized return = (1 + 0.3139)^(1/4) − 1 ≈ 7.06% per year

3) Entire portfolio
- Initial total cost = $2,818.14 + $19,849.50 = $22,667.64
- Current market value = $2,965.98 + $20,497.50 = $23,463.48
- Total cash received (coupons + dividends) = $780 + $5,580 = $6,360.00
- Ending wealth if sold today = $23,463.48 + $6,360.00 = $29,823.48
- Total dollar gain = $29,823.48 − $22,667.64 = $7,155.84
- Total percentage return over 4 years = $7,155.84 / $22,667.64 = 31.58%
- Annualized portfolio return ≈ (1 + 0.3158)^(1/4) − 1 ≈ 7.10% per year

If you want, I can also compute holding-period returns treating coupons/dividends as reinvested, compute IRR, or show the step-by-step arithmetic in a spreadsheet-friendly layout.