Topics worth revisiting:
Question 5 of the Chinese version: The impact of underwriting fees on project financing;
Question 6: Application of WACC and issuance fee formulas
1【English version 2 questions】
//The Chinese version is a mistranslation. Discounts and premiums are calculated differently.
According to the bond pricing model, the pretax cost of debt satisfies:
950=35*(P/A, rd, 26) + 1000*(P/F, rd, 26)
The solution is rd=0.0381
Therefore Rb=1.0381^2-2=0.0776
aftertax cost of debt为0.0776*0.65=0.05044
//The answer is correct, and the standard answer is just a calculation error.
//Q: When discounting face value FV, should we use the interest period interest rate rd or the annual discount rate RB?
//Answer: The interest period discount rate used by both CPA and Roth.
//Special reminder: In the Tsinghua 22 real question, on the pricing of tradable bonds, 9% is directly divided by 2 because Taylor expansion and simplification can only be used in the examination room. Without a calculator, there is no way to calculate the square root of 1.09.
//At this point, it’s really time to go back and read the real questions.
//Feelings from brushing up on the questions:
It is highly recommended to use excel or a financial calculator to complete investment and corporate financial management calculations.
If you don’t have a financial calculator, just use Excel. Online financial calculators cannot replace the full functionality of a real financial calculator, and I can’t carry a calculator with me all the time.
Python is good, but it’s tiring to type.
In the end, we have to do linear interpolation, which is too troublesome.
Tip: When calculating the discount rate here, you can regard the left side as the initial investment and change it to calculate the IRR, and you can solve it. Considering FV, you can copy the previous cash flow 25 times and replace the 26th cash flow with C+FV.
2【6 questions in English version】
WACC=0.55/(0.55+1)*0.07*(1-0.35)+1/(0.55+1)*0.125=0.0968
3【10 questions in English version】
1) List of equations:
0.098=0.45/(0.45+1)*Rb*(1-0.35)+1/(0.45+1)*0.13
Rb=(0.098-0.13/(0.45+1))/0.65*1.45/0.45=0.0414
This is the pretax cost of debt
2)
0.098=0.45/(0.45+1)*0.059+1/(0.45+1)*Rs
Rs=1.45*(0.098-0.45*0.059/(0.45+1)=0.11555
4 [English version 14 questions]
Debt ratio 3/7, equity ratio 4/7
1) Wrong decision-making. You need to look at the weighted average issuance costs instead of individual costs; then consider costs such as interest.
//Just take a look at the answer. Don't take it seriously.
Considering purely from the financing cost, for the same financing amount, the issuance fee of full debt financing is the lowest. In order to maximize shareholder wealth, a company must minimize project financing costs.
2) Weighted average issuance fee f0=3/7*0.02+4/7*0.06=0.0429
3) The true cost means that after taking into account the issuance expenses, the actual funds raised = 35/0.9571 = 36.5688.
If all-debt financing is still adopted, the issuance fee will still be lower than the weighted average issuance fee. Therefore, from a financial perspective, this plan is feasible.
//Attached is a discussion on whether corporate bond issuance underwriting fees can be tax deductible
Relatively complicated. If the textbook does not deduct tax for this subject, then it will be calculated according to the textbook. In practice, listen directly to the leader.
//Thinking: Why does this project only consider issuance costs and not the cost of stocks and bonds themselves?
//Answer: Combined with question 5, examine your understanding of the nature of F and why average underwriting fees can be used.
5【English version 18 questions】
//First, open up the two chapters of project valuation and securities valuation.
If a company wants to make money, it invests in projects; if it wants to invest in projects, it needs financing.
Project investment amount = financing amount //All behaviors are from the company’s perspective
The reason why p*(1-f0) is needed is because only by increasing the financing amount can the project cost be covered.
//Next derive the average underwriting fee.
Part of the equity financing, part of the bond financing, and the underwriting fee add up to the total issuance fee.
(Project cost + issuance fee) (1-F) = project cost
Project Cost - F*Project Cost + Issuance Fee - Issuance Fee*F = Project Cost
Issuance fee = (project cost + issuance fee)*F
The solution is weighted average underwriting fee = issuance fee / (project cost + issuance fee)
// Therefore, the total issuance fee of stocks and bonds cannot be directly divided by the project cost, because the underwriting fee will be calculated high.
//This question first finds f0
//Method 1: Get it right in one step:
f0=1.15/(1.15+19)=0.0571
//Method 2: Step by step derivation with reference to the standard answers:
The actual financing amount of the project = project cost + total issuance fee = 1.15 + 19
Let the weighted average issuance cost be f0
Then (1.15+19)*(1 - f0) = 19
The solution is f0= 1 - 19/(1.15+19) = 1.15/(1.15+19)=0.0571
//Second, find the property rights ratio
//Method 1: Get it right in one step
Let the property rights ratio be B/S
The debt ratio is B/VL and the equity ratio is S/VL
0.0571=0.03*B/VL+0.07*S/VL
Multiply both sides by VL/S to get 0.0571*VL/S = 0.03*B/S + 0.07 //The goal is to find the denominator Items withS
Expand to get 0.0571+0.0571*B/S = 0.03*B/S + 0.07
B/S=(0.07-0.0571)/(0.0571-0.03)=0.4760
//Method 2: Step-by-step method, use investment symbols to set the debt-to-equity ratio
Assume that in the target capital structure, the proportion of debt is wD and the proportion of new shares is 1-wD
0.0571=wD*0.03+(1-wD)*0.07
The solution is wD=(0.07-0.0571)/0.04=0.3225
Target property rights ratio B/S=0.3225/(1-0.3225)=0.4760
//Incorrect explanation: When considering underwriting fees, divide by the original cost of the project
Since the capital structure remains unchanged after the issuance of securities, the weighted average issuance fee is calculated as:
f0=1.15/19=0.0605
Assume that in the target capital structure, the proportion of debtwD and the proportion of new shares1-wD< /span>
0.0605=wD*0.03+(1-wD)*0.07
解得wD=(0.07-0.0605)/0.04=0.2375
Medicine weight ratioB/S=0.2375/(1-0.2375)=0.3115
6 [English version 22 questions]
//This question is very interesting, it is already a level of difficulty. After joining the investigation of working capital management, the biggest difficulty is the understanding of accounts payable.
//Q: Shouldn’t NPV be an independent decision from financing?
//Answer: It is indeed calculated separately, but WACC is used when discounting, so it is together with the capital budget. The problem is AP.
//Q: Accounts payable are considered financing income or cost outflow?
//Saving money comes at the cost of paying it back in the future, which is essentially borrowing for financing. It is the same as the central bank's OMO reverse repurchase and repo withdrawal. In other words, it has nothing to do with NPV.
//In the calculation of weighted average capital, the cost of liabilities is the weighted average of short-term liabilities (operating liabilities) and long-term liabilities. The essence reflected here is: 1. Market value rather than book value is used to measure capital structure; 2. Short-term liabilities are also counted as liabilities, and can be included in the weighted average of liabilities, or counted separately in the total; preference shares are not necessarily taken out. Calculated alone, it can also be put together with common stocks to make a weighted average S. If this part is not considered, WACC will be exaggerated and PV will be smaller.
//In issuance expenses, short-term liabilities also account for a small part of the total and must be taken into consideration, otherwise the estimated cash flow will become larger.
First, to estimate the cash flow, you need to calculate the weighted average issuance fee.
The debt-to-equity ratio is 0.55, and liabilities include long-term liabilities and short-term (operating) liabilities.
Weighted average liability underwriting fee=0.2/(1+0.2)*0+1/(1+0.2)*0.04=0.0333
Weighted average issuance fee f0=1/(0.55+1)*0.08+0.55/(0.55+1)*0.0333=0.0634
Therefore, considering the issuance costs, the initial investment of the project is 50/(1-0.0634)=53.3846 mln USD
Second, estimate the project discount rate. For photographic equipment manufacturing companies, project risk is equivalent to company risk, so it is directly discounted using the weighted average cost of capital.
The company's management believes that WACC can be used to measure the cost of short-term liabilities.
Among them, new bonds are issued at par, so the cost of debt capital is the coupon rate of 0.08
From this we can get the equation:
WACC=1/1.55*0.14+0.2/1.2*0.55/1.55*WACC+1/1.2*0.55/1.55*0.08*0.65
//Simplify the computer-based test by typing directly, otherwise you won’t be able to calculate it even if you type on the calculator for half an hour
WACC=0.0903+0.0591*WACC+0.0154
0.9409*WACC=0.1057
Solve to get WACC=0.1123
//hint:
1. The difference between WACC and f0: interest is tax deductible. WACC’s RB must be after tax
2. Don’t forget that B/S is not B/VL, and the same is true for S.
Finally calculate the project NPV.
NPV=-52.8346+6.7/0.1123=6.8170 mln USD
This item is acceptable.
//The following is a wrong solution
Idea: Based on the company's capital structure, consider issuance fees for financing. From this basis, annual operating cash flow is reduced by the cost of accounts payable.
The weighted average issuance fee isf0=0.55/1.55*0.04+1/1.55*0.08+0= 0.0658
late early stage growth book50/(1-0.0658)=53.5217
Price per year53.5217*(0.55/1.55)*0.2=3.7983
After sorting out the cash flows, let’s calculate the discount rate.
New bonds are issued at par, so the bond capital cost is the coupon rate0.08
The weighted average capital isWACC=0.55/1.55*0.08*(1-0.35)+1/1.55*0.14=0.1088
Below the bottomWACCThe first item is opened.
NPV=-53.5217-3.7983/0.1088+6.7/0.1088=-26.8516
Therefore, the manufacturing plant project should be abandoned.