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

What would you like computed from this information? Common useful results are (a) the dollar cash flows and current market value of Sam’s holdings, (b) the holding-period return over the 4 years, and (c) the annualized (geometric) return. Below I give those (assuming coupons/dividends were taken as cash and not reinvested).

Calculations and results

Inputs / unit values
- Bond par = $1,000; purchase price = 93.938% = $939.38; current price = 98.866% = $988.66.
- Bond coupon = 6.5% of par = $65 per bond per year.
- Bonds held = 3.
- Stock purchase price = $44.11; current price = $45.55.
- Shares held = 450.
- Dividend = $3.10 per share per year.
- Holding period = 4 years.

Per-asset cash flows and market values
- Bonds:
- Initial cost = 3 × $939.38 = $2,818.14.
- Coupon receipts over 4 years = 3 × $65 × 4 = $780.
- Current market value = 3 × $988.66 = $2,965.98.
- Total realized + current value = $2,965.98 + $780 = $3,745.98.
- Holding-period return (4 years) = ($3,745.98 − $2,818.14)/$2,818.14 = 32.95% (≈32.95%).
- Annualized (geometric) return ≈ 7.39% per year.

- Stock:
- Initial cost = 450 × $44.11 = $19,849.50.
- Dividend receipts over 4 years = 450 × $3.10 × 4 = $5,580.
- Current market value = 450 × $45.55 = $20,497.50.
- Total realized + current value = $20,497.50 + $5,580 = $26,077.50.
- Holding-period return (4 years) = ($26,077.50 − $19,849.50)/$19,849.50 = 31.36%.
- Annualized (geometric) return ≈ 7.06% per year.

Portfolio totals
- Initial total investment = $2,818.14 + $19,849.50 = $22,667.64.
- Total cash receipts over 4 years (coupons + dividends) = $780 + $5,580 = $6,360.
- Current total market value = $2,965.98 + $20,497.50 = $23,463.48.
- Total ending wealth (market value + cash received) = $23,463.48 + $6,360 = $29,823.48.
- Total holding-period return (4 years) = ($29,823.48 − $22,667.64)/$22,667.64 = 31.584% (≈31.58%).
- Annualized (geometric) portfolio return ≈ (1.31584)^(1/4) − 1 ≈ 7.11% per year.

If you want: I can (1) recompute assuming dividends/coupons were reinvested, (2) show the step-by-step arithmetic, or (3) compute the bond yields-to-maturity at purchase and now (I would need the bond’s maturity date/remaining years). Which would you like?