Question

Can you assist with the following? What formulas should I use for these questions and what does it all mean? I want to be better at this, but I just can't seem to understand.

A firm can get $1,000,000 in exchange of 25% of its equity. After investing the amount raised in the firm, the firm expects to generate $300,000 in FCF next year, which is expected to grow at 3% in perpetuity after that.

Before closing the deal, Mr. Wonderful approaches the firm and argues that he is willing to provide the $1,000,000 but since he is “smart capital”, he requests 40% of the equity of the firm.

c) Calculate the cost of Mr. Wonderful capital for the firm if he does not intervene in the firm’s operations (i.e., assuming that the firm’s cash flows are as described above). How is this cost of capital related to the WACC of the firm?

d) Suppose now that Mr. Wonderful affects the firm’s cash flows, i.e., he can accelerate firm’s growth to 5% for the first 5 years. After that, the firm’s cash flow will grow at 3% in perpetuity.
Calculate the cost of Mr. Wonderful capital to the firm. How does this cost relate to the WACC of the firm?

e) Is Mr. Wonderful a desirable source of funds for the owners of the firm?

f) Suppose that Mr. Wonderful is able to make the firm grow at k% rather than 3% for the first five years. Find the rate of growth that would leave the firm indifferent between bringing Mr.
Wonderful as a source of capital to the firm.

Answer 1

1,000,000 USD in exchange for 25% stake in the company .

This means that the post money valuation = Investment / Stake = 1,000,000 / 25% = 4,000,000 USD

Pre Money valuation = Post Money Valuation - Investment = 3,000,000

FCF1 = 300,000

Growth rate = 3% till perpetuity

Mr. Wonderful proposes 1,000,000 USD for 40% stake in the company.

This means that the post money valuation = Investment / Stake = 1,000,000 / 40% = 2,500,000 USD

Pre Money valuation = Post Money Valuation - Investment = 1,500,000

Answer C)

Cost of Mr. Wonderful's Capital

Value of Firm = FCF at end of year 1 / Cost of equity - Growth %

2,500,000 = 300,000 / Cost of Equity - 3%

2,500,000 * (Cost of Equity - 3%) = 300,000

2,500,000 * Cost of Equity - 75,000 = 300,000

2,500,000 * Cost of Equity = 375,000

Cost of Equity =  375,000 / 2,500,000

Cost of Equity = 15%

Answer D)

Cash Flows with support of Mr. Wonderful grow at 5% for First 5 years

Year 1	Year 2	Year 3	Year 4	Year 5
300,000	315,000	330,750	347,288	364,652

Value of firm at end of 5th year = Value * (1+Growth%)^n

= 2,500,000 * (1.05)^5

=3,190,704 USD

Value of Firm at end of 5th year = FCF at end of year 6 / Cost of equity - Growth %

3,190,704 = 364,652*(1.03) / Cost of Equity - 3%

3,190,704  = 375,591.43 / Cost of Equity - 3%

3,190,704 * Cost of Equity - 95,721.11 = 375,591.43

3,190,704 * Cost of Equity = 471,312.55

Cost of Equity = 471,312.55 / 3,190,704

Cost of Equity = 14.77%

Answer E)

Yes, mr. wonderful is a reliable source of funds for the entrepreneur, even though his cost of capital is higher than other investors. This is because of the following reasons:

GUIDANCE AND EXPERTISE:

Mr. Wonderful would already have rich experience in creating and taking start-ups to the next level, their expertise and guidance can prove to be useful for the entrepreneur. Mr. wonderful can help with strategy consulting, technical assistance, resources, etc. in order to make the venture successful.

HELP IN FORM OF CONNECTIONS, HIRING NEEDS, ETC.

MR. Wonderful will bring his entire valuable and unmatched network on the table given the huge equity holding in the company. They also have huge connections in the industry and connect you with suppliers to reduce your costs of production or servicing, cheaper raw materials, etc. or can connect you with right people needed for your organisation such as android developers, marketers, etc.

RAPID GROWTH

Conencting with Mr. Wonderful will grow your startup/venture at a higher rate than what the other investors can help in or you would have achieved yourself.