Question

Sage Hill Inc. owns 25% of the common shares of Sheffield Corp. The other 75% of the shares are owned by the Sheffield family. Sage Hill acquired the shares eight years ago through a financing transaction. Each year, Sage Hill has received a dividend from Sheffield. Sheffield has been in business for 60 years and continues to have strong operations and cash flows. Sage Hill must determine the fair value of this investment at its year end. Since there is no market on which the shares are traded, Sage Hill must use a discounted cash flow model to determine fair value.

Sage Hill management intends to hold the shares for 5 more years, at which time they will sell the shares to the Sheffield family under an existing agreement for $1 million. There is no uncertainty in this amount. Management expects to receive dividends of $90,000 for each of the five years, although there is a 20% chance that dividends could be $45,000 each year. The risk-free rate is 3% and the risk-adjusted rate is 5%.

Calculate the fair value of the investment in Sheffield using the traditional approach. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. Round answers to 0 decimal places, e.g. 5,275.)

Calculate the fair value of the investment using the expected cash flow approach. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. Round answers to 0 decimal places, e.g. 5,275.)

Answer 1

Solution the investment in Sheffield Calculation of fair value of using traditional approach: Annual cash expected = $90000 *[pv factor of annuity, 5 years, 5.1.) : $ 90000 4-32948 [referred table • $389653 proceeds. expected sale at the end of plus the year 5! = $ 1000000 X (PV factor of lump sum , 5 years, 5v.) = $ 1000000 x 0.78353 (reffered table] • $ 783530 Hence, investment & above sum of The fair values of two amounts. 1. e) $389653 + $783530 =>$1173183.

investment using the calculation expected of cash fair value of How approach: under the expected adjusted for risk and free rate. Since the rille expected. cash flow appach, cash flower are are discounted at the risk cash flows already incorporate In this can there is an 80% chance divends of & 90000 will be received and they a 20% chance 0911 be $ 45000 weighted The probability annual cash flow is a $ 90000 X 80 - = 472000 $9000 $ 25000 X 20 %. 4 81000 DH counted the cash flows Annual canh How : $81000 * (pv factor of annuity, 5 years , 301) - $ 81000 x 4.579 71[reffered table] $ 370956.51 = $370957. plus, tall proceeds expected at the end of year 5² = $ 1000000 x{PV fautor of lumpsum , syears, 3-) = $ 1000000 x 0.8626! [referred table] - $ 862610.

Hence, The fair value is the sum of the two amount: - $370951 + $862610 - $1233567. Notes: Sage Hill Inc. must consider the following terms ? (*) the amount of cash flows that are expected from the investment Dividends have been received in the past, but management would have to consider if those dividends Que expected to continue and in what amount. (x) The timing of the cash flows. Stuce cash flows will need to be discounted to a present value (pv), it is relevant to consider cohen the cash is expected to be received. (*) The risk involved in the cash flows. Sage hill need to consider the discount sale to be used in calculating the present value and whether that discount rate unds to be a risk-adjusted rate, cors if the cash Hows will be adjusted for Risk of uncertainity.