Final answer:
The value of Golf Ball Inc. when it takes the machinery upgrade is calculated to be approximately $77,007.20, considering the initial dividend of $9,000 and the present value of increased perpetual dividends of $9,140 starting from the second year discounted at a 12% rate of return.
Step-by-step explanation:
The value of Golf Ball Inc., if it undertakes the machinery upgrade, can be calculated by finding the present value of the expected perpetual dividends. Initially, the company expects to earn $10,000 per year. If the company reinvests $1,000 of its earnings into the upgrade, it will then have $9,000 to pay as dividends in the first year. Starting from the second year onwards, the upgrade will increase the earnings by $140, resulting in perpetual dividends of $9,140 per year. The present value of these dividends can be calculated using the perpetuity formula:
PV = D / r
where PV is the present value, D is the expected annual dividend, and r is the required rate of return.
For the first year, the dividend will be $9,000 and for the subsequent years, it will be $9,140. The change in value due to the machinery upgrade starting from the second year must be taken into account. The present value of the upgraded dividends starting from the second year is:
PV(upgrade) = $9,140 / 0.12 = $76,166.67
This must then be discounted back one year since the upgrade benefits begin in the second year:
PV(upgrade, discounted) = $76,166.67 / (1 + 0.12) = $68,007.20
Adding the initial $9,000 dividend:
PV(total) = $9,000 + $68,007.20 = $77,007.20
Therefore, the value of Golf Ball Inc. if it undertakes the upgrade is approximately $77,007.20.