BSOP Model在并购中的应用与折现考虑
老师您好,
请问问什么这里的合并公司的负债价值要折现呢,之前讲project的时候是Pa要折现,这里为什么Vl要折现呢?
谢谢老师
问题来源:
AFM Exam for M&A Valuation: 2010 Jun Q2
AggroChem Co is undertaking a due diligence investigation of LeverChem Co and is reviewing the potential bid price for an acquisition. You have been appointed as a consultant to advise the company's management on the financial aspects of the bid.
AggroChem is a fully listed company financed wholly by equity. LeverChem is listed on an alternative investment market. Both companies have been trading for over 10 years and have shown strong levels of profitability recently. However, both companies' shares are thinly traded. It is thought that the current market value of LeverChem's shares at 33.3333% higher than the book value is accurate, but it is felt that AggroChem shares are not quoted accurately by the market.
The following information is taken from the financial statements of both companies at the start of the current year:
|
AggroChem |
LeverChem |
|
$’000 |
$’000 |
Assets less current liabilities |
4,400 |
4,200 |
Capital Employed |
|
|
Equity |
4,400 |
1,200 |
5-year floating rate loan at yield rate plus 3% |
|
3,000 |
Total capital employed |
4,400 |
4,200 |
Net operating profit after tax (NOPAT) |
580 |
430 |
Net amount retained for reinvestment in assets |
180 |
150 |
It can be assumed that the retained earnings for both companies are equal to the net reinvestment in assets.
The assets of both companies are stated at fair value. Discussions with the AtReast Bank have led to an agreement that the floating rate loan to LeverChem can be transferred to the combined business on the same terms. The current yield rate is 5% and the current equity risk premium is 6%. It can be assumed that the risk free rate of return is equivalent to the yield rate. AggroChem’s beta has been estimated to be 1.26.
AggroChem Co wants to use the Black-Scholes option pricing (BSOP) model to assess the value of the combined business and the maximum premium payable to LeverChem’s shareholders. AggroChem has conducted a review of the volatility of the NOPAT values of both companies since both were formed and has estimated that the volatility of the combined business assets, if the acquisition were to go ahead, would be 35%. The exercise price should be calculated as the present value of a discount (zero-coupon) bond with an identical yield and term to maturity of the current bond.
Required:
Prepare a report for the management of AggroChem on the valuation of the combined business following acquisition and the maximum premium payable to the shareholders of LeverChem. Your report should:
(i) Using the free cash flow model, estimate the market value of equity for AggroChem Co, explaining any assumptions made. (9 marks)
(ii) Using the BSOP methodology, estimate the maximum price and premium AggroChem may pay for LeverChem. (9 marks)
(iii) Discuss the appropriateness of the method used in part (ii) above, by considering whether the BSOP model can provide a meaningful value for a company. (5 marks)
(i) Using the free cash flow valuation model for AggroChem (which is wholly financed by equity) we can estimate the market value:
Estimated market value = Free cash flows (FCF) × (1 + growth rate) / (cost of capital (Ke) – growth rate (g))
Note: Since AggroChem is financed wholly by equity, its cost of capital is equal to its cost of equity.
Free cash flow = NOPAT – Net reinvestment = $580 – $180 = $400
Assume: g = retention rate × cost of capital (Ke)
Taking the net reinvestment as a ratio of NOPAT we obtain the retention ratio (b):
b = $180/ $580 = 31.03%
Ke = 5% + 1.26 × 6% = 12.56%
g = 0.3103 x 0.1256 = 0.0390
Market value = $400,000 (1.0390)/(0.1256 – 0.0390) = $4,799,000
This modelling method assumes
that the company is a going concern,
that the free cash flow model fairly represents the fair value of the business, that the discount rate has a flat term structure,
and that future growth is constant
and the growth rate is based on the assumption that retained earnings can be invested at the cost of capital.
In practice one or more of these assumptions may be violated.
(ii) The exercise price is determined by an equivalent zero coupon bond. LeverChem’s debt is a variable rate loan; the yield is the current rate of 8%. The equivalent zero coupon debt with a term to maturity of five years is as follows:
$3 million × 1.08-5= $2.04175 million
To value the equity of the combined business as a call option we take the following as the inputs into the model:
The underlying assets of the business = $8.6 million assuming fair values
The exercise price = $2.04175 million
Risk free rate = 5%
Time to exercise = 5 years
Volatility = 0.35
Applying the BSOP Model:
d1=[In(8.6/2.04175)+(0.05+0.5 × 0.352) × 5]/(0.35 × 51/2)
d1 = 2.548
d2 = 2.548-(0.35 × 51/2)
d2 = 1.765
N(d1)= 0.9946
N(d2)= 0.9612
Call value = $8.6m × 0.9946 - $2.04175 × 0.9612 × e-0·05×5 = 8.55356 - 1.52842 = 7.02514
The value of the call on the combined firm's assets is approximately $7.025 million.
Deducting AggroChem's current equity
$7.025m - $4.799m= $2.226m
This suggests that the maximum price which should be paid to the shareholders in LeverChem is $2.226m.
Market value of LeverChem = $1,200,000 × 1.331/3 = 1,600,000
Maximum premium payable $626,000 or just over 39%.
(iii) Although the BSOP model is very effective in valuing continuously traded securities in active markets, its validity is more questionable where the basic assumptions supporting the model do not hold. It is assumed that the value of the assets of the business change randomly around a rising trend and are thus log-normally distributed. It is also assumed that they are traded in frictionless markets and the holding can be continuously adjusted. Finally, the model is only appropriate for European style options. Given these assumptions, the modelling can only be expected to give an indicative rather than a definitive value, but in the absence of any alternative is a useful adjunct to commercial judgement.
王老师
2021-10-16 19:58:24 813人浏览
这里需要注意,是否需要折现主要考虑的是哪个时间点,如果考虑的不是现在这个时间点,而是以前的时间点,则数据均要折现。
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