Question

1. Mambo Leo Ltd has a cost of equity of 10%. Currently the company has 250,000 shares which are quoted at the securities exchange at $120 per share. The Company’s earnings per share is $10 and it intends to maintain a dividend payout ratio of 50% at the end of the current financial year. The expected net income for the current year is $3 million and the available investment proposals are estimated to cost $ 6 million.

Required

Using the Modigliani and Miller (MM) Model, calculate the value of the firm if:

1. Dividend is paid
2. Dividend is not paid

Comment the results above

Answer 1

Let us first summarize all the given points for an easier calculation.

Given:

Current Market Price (P0) = $120

Cost of Equity(Ke) = 10%

Dividend at the end of the year( D1)= Dividend payout ratio * Earnings per share

= 50% * $10 = $5

We will first calculate the Expected price at the end of the year i.e. P1 for both the cases (Dividend paid and not paid)

1. If Dividend of $5 is paid

Under MM Model,

P0 = 1/ (1+ke) * (D1+ P1)

where,

P0 is the current Price

Ke is the cost of equity

D1 is the Dividend at the end of year

P1 is the price at the end of year

This implies that, P0 (1 + ke) = D1 + P1

P1 = P0 (1+ ke) - D1

= 120( 1.10) - 5

= $127

2. If Dividend of $5 is not paid

P1 = P0 (1 + Ke) - D1

= 120(1.10)

= $132

CALCULATION OF VALUE OF THE FIRM UNDER BOTH THE CASES

1. If Dividend is paid

Given:

Total Earnings(Income) = $3,000,000

Dividends paid (Outstanding shares * Dividend per share) , 250,000* 5 = $1,250,000

Retained earnings can be computed as Total Income - Dividends paid

= 3,000,000 - 1,250,000

= $1,750,000

Investment cost = $6,000,000

According to the MM model,

If the company has 'n' number of shares outstanding, then the value of the firm becomes n times the current market price i.e nP0 . The nP0 is computed as:

where, Ke is the cost of equity

n is the number of outstanding share

m is the fresh shares issued for the new investment opportunity

P1 is the price at the end of year 1

I is the Investment cost

E is the total earnings

The fresh capital that the firm issues is the Total investment cost less the Retained earnings

Therefore, fresh capital = 6,000,000 - 1,750,000

= 4,250,000

We computed the P1, as $127

Fresh issue number of shares 'm ' = 4250000/127

Therefore, m = 33,464.56

n + m = 2,50,000+ 33,464.56

= 283464.56

nP0 = 1/ (1+ke) * [ (n+m)P1 - I + E]

= 1/ (1.10) * [ (283464.56) *127 - 6,000,000 + 3,000,000]

= 1/ (1.1) * [ 36,000,000 - 6,000,000 + 3,000,000]

= 1/ (1.1) * [33,000,000]

= $30,000,000

2. If Dividend is not paid

Given,

Total Earnings = $3,000,000

If Dividend is not paid, the retention ratio would be 1.

Retained earnings = $3,000,000

Investment cost = $6,000,000

Therefore, fresh capital = 6,000,000-3,000,000

= 3,000,000

we computed P1 as $132 in this case

m = 3,000,000/ 132

= 22727.27

m + n = 250,000 + 22727.27

= 272727.27

Therefore, nP0 = 1/ (1.10) * [ 272727.27(132) - 6000000 + 3000000]

= 1/(1.1) * [ 36000000 - 3000000]

= $30,000,000

COMMENTS: It can be seen that the value of the firm comes out to be the same in both the cases i.e whether Mambo Leo Ltd pays the Dividends or it does not pay the dividends. This is what the Modigliani and Miller approach shows, that the Dividend policy is irrelevant for the valuation of the firm.