A relocation of a short stretch of rural highway feeding into Route 390 northwest of Dallas is to be made to accommodate new gro
wth. The existing road is now unsafe, and improving it is not an alternative. Alternate new route locations are designated as East and West. The initial investment by government highway agencies will be $3,650,000 for East and $5,000,000 for West. Annual highway maintenance costs will be $120,000 for East and $90,000 for the shorter location West. Relevant annual road user costs, to be treated as disbenefits, considering vehicle operation, time en route, fuel, safety, mileage, and so on, are estimated as $880,000 for East and only $660,000 for West. Assume a 20-year service life and i = 7% / year. Compute the incremental B/C ratio and decide whether East or West should be constructed.
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Answer:
- <u>15.7%</u>
Explanation:
The <em>price</em> of a <em>stock</em> can be modeled by the present value of the stream of future <em>dividends</em> discounted at a rate equal to the<em> return expected</em>.
The equation, when the dividends are expected to <em>grow</em> at a constant rate, less than the return rate is:
Where:
- Price₀ is the <em>current price</em>: $44.12
- Div₁ is the <em>dividend </em>to be paid a year from now: $0.46 × 1.145 = $0.53
- g is the expected constant <em>growth rate</em>: 14.5% = 0.145
- r is the <em>expected return</em>
Then, you can solve for r: