General and supplementary information:
The paper consists of 3 problems with associated subproblem. The problems can be solved independently of each other. The stated weight for each assignment is stated solely for assisting the student's time for answering the problems. The weighting is not binding for the grading, as the grade will be determined based on the degree of goal achievement, cf. the following important text with excerpts from the goal description in the course description:

”The student must be able to account for theory and carry out analyzes in relation to the subject content, cf. the course description. When accounting for theory and doing the analysis, the student must be able to explain very clearly the preconditions and the individual elements of the analysis by means of explanatory text and by specifying the formulas used and explaining how they are used to solve the problems.”

The answer must thus contain the necessary explanatory and elaborate text and, moreover, appear clear. Prerequisites, formulas and arguments must also be clearly stated in the answer. This means that even if the standard functions in Excel or in other calculation programs are used, the theoretical formula must be stated. This also means that you must specify the variables that are included in the answer and insert- ed into the formulas used.

When the theoretical formula is stated, the specific formula number from the syllabus literature and formula list must as a minimum be stated. If appropriate, the formula itself can also be copied into the answer. Formulas from sources that are outside of curriculum literature must not be used unless the formula uses notation consistent with the formula list and syllabus literature and problems.

It must also be stated which notation is used in the answer, cf. note on the two main types of notation. The chosen notation must as far as possible be consistent through- out your answer. In addition, one must be able to clearly distinguish between input data (e.g. information from assignment text), intermediate calculations and final answers (facit).

All final answers (facit), which are numerically larger than 1, must be specified with a minimum of 4 decimals unless they are money amounts, where the final answer must be given with two decimal places. All final answers that are numerically smaller than 1 must be specified with a minimum of 4 significant digits. Remember that no intermediate calculations must be rounded off, as the final answer will thereby be inaccurate.

Problem 1 Textbook P61 and Section 15.3
The firm Recap Inc. is today (just before t=0) an all equity firm (the firm has no debt) All outstanding shares of the firm are listed on the Stock Exchange. The number of outstanding shares is 17 million. The market price of a share is today (just before t=0) DKK 16,25.

The firm is now (t=0) considering publishing a recapitalization plan for the firm. The plan entails that the company at t=0 will take out a perpetuity loan at a price equal to DKK 100 per DKK 100 in face value. The principal of the loan is 28 million. There are no transaction costs (fees, commissions etc.) related to the debt. After this, the firm will forever refrain from taking out any further debts. The proceeds from the loan will be used to repurchase some of the existing shares in the firm immediately after t=0.

The firm's marginal tax rate is assumed to remain constant at 20%. It is also assumed that corporate tax is the only imperfection in the capital market and that the firm does not have excess cash. Furthermore, it can be assumed that the firm's EBIT in all periods exceeds interest costs, which are fully deductible.

Problem 1.1
Calculate the market value of the firm’s unlevered assets (firm value) just before the public disclosure of the recapitalization plan. Prepare an overview of the firm's main groups of assets and liabilities and their values at this specific time.

Problem 1.2
Calculate the market value of the firm's levered assets immediately after the loan is taken out, i.e. at t = 0, but before the debt proceeds are used to repurchase existing shares in the firm. Prepare an overview of the firm's main groups of assets and liabilities and their values at this specific time.

Problem 1.3
Calculate the market price of the firm's shares immediately after the debt is taken out, i.e. at t = 0, but before the proceeds are used to repurchase some of the firm´s existing shares.

Problem 1.4
Calculate the number of shares that the firm repurchases.

Problem 1.5
Calculate the market value of the firm's levered assets immediately after the repurchase. Prepare an overview of the firm's main groups of assets and liabilities and their values at this specific time.

1 A loan with permanent debt. No repayments are made.
2 Face value is also named the principal of the bond or the nominal value of the bond.
3 Must include the value (PV) of any imperfections.
4 Market price per share.
5 Must include the value (PV) of any imperfections.

Problem 1.6
Determine the market price of the firm's shares immediately after the repurchase of shares.

Problem 2
Webinar 2 and Ex. 38 and 40

Ignore taxes in this problem. All budget data is provided in real terms with January 1, 2019 as the base.
Niels Net is currently working in a bicycle shop in Kgs. Lyngby, where his monthly salary is DKK 27,000 per month. Niels Net is considering starting an online store, where the product range will be electric scooters and electric skateboards. Niels Net will be the sole owner of the store.

The online store requires a relatively large storage area and associated office facilities. Niels Net has found some suitable premises west of Copenhagen for a monthly rent of DKK 32,000. Utility (electricity, water and heating) are expected to amount to DKK 6,000 per month. Expenditures (t=0) for the refurnishing and remodeling of the premises incl. IT etc. amounts to DKK 500,000. When the lease ends, the scrap value of the interior will be DKK 50,000. Renting of the premises requires payment (t=0) of a deposit equal to 3 months’ rent. Half of the deposit is expected to be repaid by the landlord when the lease ends.

Inflation is expected to be constant at 1.10% p.a. in the period 2019-2026.

In the online store there will be two sales groups: Electric scooters and Electric skate- boards.

If Niels Net does not establish his own online store, Niels Net expects to remain in his current position indefinitely. To assist in the online store, Niels Net needs to employ 2 unskilled employees for an annual salary of 310,000 kr. person.

Niels Net has established the following revenue budget for the next 8 years:

Table 2.1: Expected sales revenues (DKK 1,000 kr.)
2019 2020 2021 2022 2023 2024 2025 2026
Electric scooters
1,000
1,500
1,800
2,100
2,400
2,700
3,000
3,300

Electric skateboards
700
1,200
1,500
1,800
2,100
2,400
2,700
3,000

Gross profit margins for electric scooters are expected to be 45%. Gross profit mar- gins for Electric skateboards is expected to be 55%.

It is expected that the end of the year's stocks within each product group will amount to 20% of cost of goods sold next year.

Beginning stocks January 1, 2019 of both product groups equals 20% of cost of goods sold in 2019. The last year (2026) ending stocks are expected to be unchanged com- pared to the ending stocks the year before.

It is expected, that the net working capital (NWC) is realized at the end of the budget period.

All sales and purchases of goods are expected to occur in cash and it can be assumed that all payments are made at the end of the budget period. Capital Expenditures will be paid January 1, 2019 (t=0).

To finance the investment and start-up, Niels Net takes an 8-year fixed-rate annuity bond loan with a principal of DKK 700,000. The coupon rate of the loan is 5.0% per year and the price is 96.10 kr. per 100 kr. in face value. The loan has yearly installments (yearly payments) and it is assumed that there are no transaction costs (fees, commissions etc.) in connection with taking out the loan.

Niels Net has estimated that the market risk of the investment is such that the real risk premium should be set at 14% calculated annually. The real risk-free rate is 0.5% calculated annually.

Niels Net will only make the investment, i.e. establish the online store if it is profitable over a period of 8 years from 2019 to 2026.

Problem 2.1
Calculate the cash flow (per DKK 100 in face value) for the loan and calculate the annual effective yield9 of the loan.

Problem 2.2
Calculate the contribution margin and EBITDA in real terms for the investment in each of the 8 years in the period 2019-2026 with January 1, 2019 as base.

Problem 2.3
Calculate then the change in net working capital (∆NWC) in real terms for each of the 8 years in the period 2019-2026.

6 Gross profit = Sales – Cost of goods sold. Contribution = Sales – Variable costs. I this problem the firm (the online store) is a trading company. Please note that the only variable costs of the online store in this problem are the costs of goods sold. Because of this the Gross profit margin equals the Contribution mar- gin.
7 Nominal rate.
8 For each term state: a) outstanding debt at beginning of period, b) repayment, c) interest payment, d) total payment and e) outstanding debt end of period.
9 Also named the yield to maturity (YTM) or promised yield or IRR of the loan.

Problem 2.4
Calculate the total investment costs at t=0 (January 1, 2019) and then calculate the free cash flow (FCF) in real terms from the investment for each of the 8 years in the period 2019-2026 with January 1, 2019 as the base.

Problem 2.5
Calculate the free cash flow (FCF) of the investment in nominal terms for each of the 8 years in the period 2019-2026.

Problem 2.6
Calculate the cash flow to the creditors in nominal terms from the investment, both per January 1, 2019 (t=0) and for each of the 8 years in the period 2019-2026 and then calculate the IRR of this cash flow.

Problem 2.7
Calculate the cash flow to owners (i.e. the cash flow to Niels Net) in nominal terms from the investment both per January 1, 2019 and for each of the 8 years in the period 2019-2026.

Problem 2.8
Calculate the value of the online store per January 1, 2019 (t=0) if Niels Net makes the investment.

Problem 2.9
Calculate the value of the equity per January 1, 2019 in the online store if Niels Net makes the investment.

Problem 2.10
Calculate the capital structure weights of equity and debt in the online store per January 1, 2019 if Niels Net makes the investment.

Problem 2.11
Calculate the Net Present Value (NPV) of the investment and make a reasoned ac- count of whether NPV depends on whether the calculation of NPV is based on FCF cal- culated in real or nominal terms.

Problem 2.12
Make a reasoned account of whether Niels Net should make the investment. The ac- count must include some few and central sensitivity calculations.

Problem 2.13
Make a reasoned account of whether the discount rate of the investment depends on how much debt Niels Net raises to co-finance the investment.

10 VL, i.e. the value of the assets (firm value).

Problem 3
Currently the firm WorkSmart has no debt. However, WorkSmart plans to take up new debt, and therefore considers issuing and selling fixed-rate corporate bonds with a maturity of 8 years. The loan will be a coupon loan. The annual coupon rate of the corporate bonds is 8%. The price of the bond is DKK 96 per DDK 100 in face value.
The bonds have annual terms. Ignore taxes and fees. The rating of the bonds will be BB, cf. table 12.2. Bonds with similar maturity and corresponding amortization but having an AAA rating have a nominal annual promised yield of 0.9%.

It is assumed that the expected loss rate on the new bonds in WorkSmart is 35% under average business cycles and 60% under recessions.

Furthermore, it can be assumed that the nominal annual market risk premium is 6% calculated throughout average business cycles and 7.2% calculated throughout recessions.

Problem 3.1
Calculate the cash flow (per DKK 100 in face value) of the bonds.

Problem 3.2
Calculate the annual yield to maturity of the bonds.

Problem 3.3
Calculate for both average business cycles and for recessions the nominal expected return of the bonds using formula 12.7.

Problem 3.4
Calculate for both average business cycles and for recessions the nominal expected return of the bonds using CAPM and estimating by rating.

Problem 3.5
Calculate for both average business cycles and for recessions the nominal expected return of the bonds using CAPM and estimating by maturity.

Problem 3.6
Calculate for average business cycles the nominal spread of the bonds in WorkSmart compared to AAA rated debt using formula 12.7.

General and supplementary information: The paper consists of 3 pro...