Question

Julio de la Renta, an analyst at Blackwell Investment group is preparing a dividend forecast for Yokohama Industries for the next five years. Julio uses the following model assumptions: Sales are $100 million in the first year. Sales are expected to grow by 20% in the second year, 15% in year three, and 10% in years 4 and 5. Earnings before interest and taxes (EBIT) are 20% of sales in the first and second years, respectively. EBIT is 18% of sales in the third year, and 16% of sales in Years 4 and 5. Interest charges are 10% of total debt for the current year. The income tax rate is 40%. Yokohama pays out 20% of earnings in dividends in the first and second years, 30% in the third year, 40% in Year 4, and 50% in the fifth year. Retained earnings are added to equity in the following year. Total assets are 80% of the current year’s sales in all years. In the first year, debt is 40 million and shareholder’s equity is $40 million. Debt equals total assets less shareholders’ equity. Shareholders’ equity will equal prior year’s shareholders’ equity plus the addition to retained earnings from the prior year. Yokohama has 4 million shares outstanding. The risk-free rate is 4%. The shares of Yokohama have an estimated beta of 1.2, and the equity risk premium is estimated at 6%. The value of the company at the end of the fifth year is expected to be 10 times earnings. Your task is to help Julio de la Renta estimate Yokohama’s current value per share.

How do you calculate the cash flows and the terminal value for share for this problem?

Answer 1

All financials below are in $ mn.

Let's start the P&L projections. We should not face any problem till the level of EBIT. Please see the table below. Please see the remarks column to understand what has been done in each row.

Year		1	2	3	4	5	Remarks
Parameter	Linkage
Sales	S	100.00	120.00	138.00	151.80	166.98	120 = 100 x (1 + 20%); 138 = 120 x (1 + 15%) and so on
y-o-y growth	g		20%	15%	10%	10%	Given in question
EBIT Margin		20%	20%	18%	16%	16%	Given in question
EBIT		20.00	24.00	24.84	24.29	26.72	Sales x EBIT Margin

In order to proceed beyond this, we need interest expenses in place. For interest we need debt level.

For year 1:

Total assets are 80% of the current year’s sales in all years. In the first year, debt is 40 million and shareholder’s equity is $40 million. Debt equals total assets less shareholders’ equity. Shareholders’ equity will equal prior year’s shareholders’ equity plus the addition to retained earnings from the prior year.

Asset, A = 80; Equity, E = 40 and Debt, D = 40

Interest expense = 10% of current year's debt = 10% x 40 = 4

Hence, we can now do the calculations for year 1, as shown below: Please see the Linkage column and the remarks column

Year		1	2	3	4	5	Remarks
Parameter	Linkage
EBIT	EBIT	20.00	24.00	24.84	24.29	26.72	Sales x EBIT Margin (Last row of the table above)
[-] Interest	I = 10% x D	4.00					10% x Debt calculated several rows below
EBT	EBIT - I	16.00					EBIT - Interest expenses
Taxes	40% x EBT	6.40					40% of pre tax earnings
Net income	NI = EBT - Taxes	9.60					Pre tax earnings - taxes
Dividend payout	DPO	20%	20%	30%	40%	50%	Given in question
Dividends paid	D = NI x DPO	1.92					Net income x dividend payout ratio
Addition to Equity	AE = NI - D	7.68					Net income - dividends
Total Assets	A	80.00	96.00	110.40	121.44	133.58	80% x Sales
Equity	E	40.00	47.68				47.68 = Equity in year 1 + Addition to equity in year 1 = 40 + 7.68
Debt	D = A - E	40.00	48.32

It's important for us to understand the equity and debt calculation for year 2.

Once we have calculated the figure corresponding to Addition to Equity at the end of year 1 as shown above, we need to recall that:

Shareholders’ equity in subsequent year will equal prior year’s shareholders’ equity plus the addition to retained earnings from the prior year.

Hence, equity for year 2 = equity for year 1 + addition to equity in year 1 = 40 + 7.68 = 47.68. Asset in year 2 is known and is = 96 (please see the table above, it's 80% of sales in year 2).

Now recall, Debt equals total assets less shareholders’ equity. Hence, debt in year 2 = Asset in year 2 - equity in year 2 = 96 - 47.68 = 48.32

Hence, we can now calculate interest for year 2 = 10% of debt = 10% x 48.32 = 4.832 and complete the loop for year 2 to get addition to equity at the end of year 2. From there we will calculated equity for year 3 and so on...After couple of loops, we should end up getting the following table:

Year		1	2	3	4	5	Remarks
Parameter	Linkage
EBIT	EBIT	20.00	24.00	24.84	24.29	26.72	Sales x EBIT Margin
[-] Interest	I = 10% x D	4.00	4.83	5.35	5.64	6.18	10% x Debt calculated several rows below
EBT	EBIT - I	16.00	19.17	19.49	18.65	20.54	EBIT - Interest expenses
Taxes	40% x EBT	6.40	7.67	7.80	7.46	8.21	40% of pre tax earnings
Net income	NI = EBT - Taxes	9.60	11.50	11.69	11.19	12.32	Pre tax earnings - taxes
Dividend payout	DPO	20%	20%	30%	40%	50%	Given in question
Dividends paid	D = NI x DPO	1.92	2.30	3.51	4.48	6.16	Net income x dividend payout ratio
Addition to Equity	AE = NI - D	7.68	9.20	8.18	6.71	6.16	Net income - dividends
Total Assets	A	80.00	96.00	110.40	121.44	133.58	80% x Sales
Equity	E	40.00	47.68	56.88	65.07	71.78	47.68 = Equity in year 1 + Addition to equity in year 1 = 40 + 7.68
Debt	D = A - E	40.00	48.32	53.52	56.37	61.80	Asset - equity

Our annual cash flows are the dividend calculated in row shown as bold in the table above.

Now we need to find:

1. Cost of equity, Ke = Risk free rate + Beta x Equity risk premium = 4% + 1.2 x 6% = 11.20%=0.112
2. Terminal value = value of the company at the end of the fifth year = 10 times earnings = 10 x Net income of year 5 = 10 x 12.32 = 123.22

Yokohama’s current value = Present value of all the future dividends discounted at cost of equity + Present value of terminal value discounted by cost of equity

where D_i = Dividend paid in year "i" and TV = terminal value at the end of year 5

Hence, Yokohama’s current value

= 85.16

Nos. of shares outstanding, N = 4 mn

Yokohama’s current value per share = Yokohama’s current value / N = 85.16 / 4 = $ 21.29 / share