Discounted Cash Flow Valuations (w/ Solutions)

Calculating Returns

Suppose a stock had an initial price of $92 per share, paid a dividend of $1.45 per share during the year, and had an ending share price of $104. Compute the percentage total return.

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is:

R = [($104 – 92) + 1.45] / $92 R = 0.1462 or 14.62%

Calculating Returns

Rework the problem above, but this time assuming the ending share price is $81.

Using the equation for total return, we find:

R = [($81 – 92) + 1.45] / $92 R = – 0.1038 or –10.38%

Holding Period Return

A stock has had returns of 18.43 percent, 16.82 percent, 6.83 percent, 32.19 percent, and −19.87 percent over the past five years, respectively. What was the holding period return for the stock?

Apply the five-year holding-period return formula to calculate the total return of the stock over the five-year period, we find:

5-year holding-period return = [(1 + R1)(1 + R2)(1 +R3)(1 +R4)(1 +R5)] – 1 5-year holding-period return = [(1 + 0.1843)(1 + 0.1682)(1 + 0.0683)(1 + 0.3219)(1 – 0.1987)] – 1 5-year holding-period return = 0.5655 or 56.55%

Calculating Returns

You bought a share of 5 percent preferred stock for $92.85 last year. The market price for your stock is now $94.63. What was your total return for last year?

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. This preferred stock paid a dividend of $5, so the return for the year was:

R = ($94.63 – 92.85 + 5.00) / $92.85 R = 0.0730 or 7.30%

Geometric Returns

A stock has had returns of 34 percent, 18 percent, 29 percent, −6 percent, 16 percent, and −48 percent over the last six years. What is the geometric return for the stock?

Using the equation for the geometric return, we find: Geometric average return = [(1 + R1) × (1 + R2) × … × (1 + RT)]1/T – 1