Marie-Josee intends to buy her father company. He wishes to sell her his company for a $850 000 amount because he would like to bequeath his inheritance to his daughter in his lifetime. Knowing the big generosity of her father, Marie-Josee wishes to make projections to estimate the company value before purchasing it. According to the book value, the company possesses 25 000 ordinary shares. Marie-Josee anticipates that the actual profit of $5,26 per action should grow to 15 % rate a year for the next 3 years. She also considers that the company should reinvest all its profits in the company during the first two years to support its growth. She plans that the company can distribute 40 % of its profits in dividends afterward. This annual dividend should grow at a 12 % rate during the next five years to decrease by 1 % afterward until the moment when the growth rate of the dividend will reach 8 % and this, infinitely. The return rate demanded by the shareholders for similar companies rise at 14 %.
a) According to those projections, what price Marie-Josse should pay to buy the company of her father?
b) Knowing that Marie-Josee really buy the company of her father $850 000, what is the value of the inheritance?
To calculate the price Marie-Josee should pay to buy her father's company, we need to estimate the future cash flows of the company and discount them to the present value using the required return rate of 14%.
Let's break down the steps to calculate the price:
Step 1: Calculate the future cash flows for the next three years.
- The company is expected to grow its profit per share at a rate of 15% per year.
- The initial profit per share is $5.26, so the future profits per share for the next three years would be:
Year 1: $5.26 * (1 + 0.15) = $6.04
Year 2: $6.04 * (1 + 0.15) = $6.95
Year 3: $6.95 * (1 + 0.15) = $7.99
Step 2: Calculate the dividends for the next five years.
- The company plans to reinvest all its profits for the first two years, so no dividends are paid in those years.
- Starting from year 3, 40% of the profits are distributed as dividends, and the dividend growth rate is 12% for the next five years.
Year 3: $7.99 * 0.4 = $3.20
Year 4: $7.99 * 0.4 * (1 + 0.12) = $3.58
Year 5: $7.99 * 0.4 * (1 + 0.12)^2 = $4.00
Year 6: $7.99 * 0.4 * (1 + 0.12)^3 = $4.47
Year 7: $7.99 * 0.4 * (1 + 0.12)^4 = $4.99
Step 3: Calculate the perpetual dividend growth after year 7.
- The dividend growth rate decreases by 1% each year until it reaches 8%.
- We can use a formula to calculate this:
Year 8 and beyond: $4.99 * (1 + 0.08) / (0.14 - 0.08) = $82.92
Step 4: Calculate the present value of each cash flow.
- To discount the future cash flows, we use the required return rate of 14%.
- Present value calculations involve dividing the future cash flow by (1 + required return rate) raised to the power of the number of years in the future.
Now let's calculate the present value of each cash flow:
Year 1: $6.04 / (1 + 0.14)^1 = $5.30
Year 2: $6.95 / (1 + 0.14)^2 = $5.56
Year 3: $7.99 / (1 + 0.14)^3 = $5.85
Year 4: $3.20 / (1 + 0.14)^4 = $2.43
Year 5: $3.58 / (1 + 0.14)^5 = $2.15
Year 6: $4.00 / (1 + 0.14)^6 = $1.90
Year 7: $4.47 / (1 + 0.14)^7 = $1.68
Year 8 and beyond: $82.92 / (1 + 0.14)^8 = $19.74
Step 5: Calculate the total present value by summing up all the present values.
- Total present value = $5.30 + $5.56 + $5.85 + $2.43 + $2.15 + $1.90 + $1.68 + $19.74 = $44.61
The price Marie-Josee should pay to buy the company is the total present value of the cash flows, which is $44.61.
To calculate the value of the inheritance if Marie-Josee actually buys the company for $850,000, we can subtract the purchase price from the value of the company:
Value of the inheritance = Purchase price - Price Marie-Josee should pay
Value of the inheritance = $850,000 - $44.61 = $849,955.39
Therefore, the value of the inheritance would be $849,955.39.