Finance Answer Note #1

Question 1 Masco, Inc. is considering the purchase of a new machine for $100,000. The machine will reduce manufacturing costs by $10,000 annually. Masco will use the modified accelerated cost recovery system (MACRS) accelerated method (5-year asset) to depreciate the machine and expects to sell the machine at the end of its 6-year operating life for $20,000. (The percentages for the 5-year MACRS class are, beginning with year 1 and ending with year 6, 20%, 32%, 19%, 12%, 11%, and 6%.) The firm expects to be able to reduce networking capital by $25,000 when the machine is installed, but the required working capital will return to the original level when the machine is sold after six years. Masco’s marginal tax rate is 35%, and it uses a 15% cost of capital to evaluate projects of this nature What is the initial cash outlay? What is the first year's incremental operating cash flow? What is the terminal year’s cash flow (not including the last year’s operating cash flow)? Answer The initial cash outlay for the machine is the purchase price of $100,000 minus the expected reduction in networking capital of $25,000, resulting in an initial cash outlay of $75,000. The first year's incremental operating cash flow can be calculated by subtracting the annual tax savings from the reduced manufacturing costs due to the new machine. The annual tax savings can be calculated using the MACRS accelerated method, specifically the 20% depreciation rate for the first year. This results in $100,000 * 0.20 = $20,000 in annual depreciation. Multiplying this by the firm's marginal tax rate of 35% gives a tax savings of $7,000. In addition, the reduced manufacturing costs of $10,000 also result in a tax savings of $3,500 (calculated by multiplying the cost reduction by the marginal tax rate). Therefore, the first year's incremental operating cash flow is $10,500 ($10,000 reduction in manufacturing costs + $7,000 tax savings on depreciation + $3,500 tax savings on reduced costs). The terminal year's cash flow can be calculated by taking the remaining book value of the machine (original cost - accumulated depreciation) and adding the sale price. The remaining book value after five years of depreciation is $20,000 ($100,000 - $80,000 accumulated depreciation), and the sale price is $20,000. This results in a terminal year's cash flow of $40,000. However, this does not include the last year's operating cash flow, which would be the final year's reduction in manufacturing costs and tax savings on depreciation as calculated in the first year. This would bring the total terminal year's cash flow to $53,500 ($40,000 + $10,000 cost reduction + $3,500 tax savings on reduced costs + $7,000 tax savings on depreciation). Question 2 Find the monthly payment, the amount paid, and the total interest. The mortgage is 75,000, 15 years, and rate is 7.50%. Answer To find the monthly payment, the amount paid, and the total interest for a mortgage of $75,000 with a 15-year term and a 7.50% interest rate, we can use the formula for calculating mortgage payments, which is: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]. Where: M = Monthly payment P = Principal amount (the amount borrowed) i = Monthly interest rate (annual interest rate divided by 12) n = Total number of monthly payments (number of years * 12) Step-by-Step Calculation: First, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate of 7.50% by 12 (number of months in a year). So, i = 7.50% / 12 = 0.0625. Next, we need to calculate the total number of monthly payments by multiplying the number of years, which is 15, by 12. So, n = 15 * 12 = 180. Plugging in the values in the formula, we get: M = 75,000 [ 0.0625(1 + 0.0625)^180 ] / [ (1 + 0.0625)^180 – 1 ]. Simplifying the equation, we get: M = 75,000 [ 0.0625(1.0625)^180 ] / [ (1.0625)^180 – 1 ]. Using a calculator, we get a monthly payment of $694.85. To calculate the total amount paid over the course of 15 years, we multiply the monthly payment by the total number of payments, which is 180. So, total amount paid = $694.85 * 180 = $125,073. To find the total interest paid, we subtract the principal amount of $75,000 from the total amount paid. So, total interest paid = $125,073 - $75,000 = $50,073. Question 3 A couple has been granted mortgage loan at an annual interest rate of 7 percent for 25 years. The home has a selling price of $98,750. They need a 25 percent down payment on their new home. What is the monthly payment? How much of the first monthly payment goes toward reducing the principal? Answer To find the monthly payment and the breakdown of the first payment for this mortgage loan, we need to use the formula for calculating mortgage payments. This formula is: M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ], where M is the monthly payment, P is the principal amount borrowed, i is the interest rate per month, and n is the number of months for the loan. Let's break down the given information to plug into the formula: - Principal (P) amount borrowed: $98,750 - Interest rate per month (i): 7% divided by 12 months = 0.00583 - Number of months (n): 25 years multiplied by 12 months = 300 months Substituting these values into the formula, we get: M = $98,750 [ 0.00583(1 + 0.00583)^300 ] / [ (1 + 0.00583)^300 - 1 ] = $634.29 Therefore, the monthly payment for this mortgage loan is $634.29. To find the breakdown of the first monthly payment, we need to understand how mortgage payments are calculated. In the beginning, a larger portion of the monthly payment goes towards paying off the interest, while a smaller portion goes towards reducing the principal. As the loan progresses, the ratio of interest to principal gradually shifts, with more going towards reducing the principal. To find the amount that goes towards the principal in the first monthly payment, we can use the amortization schedule. This schedule shows the breakdown of each monthly payment over the life of the loan. Using an online mortgage calculator, we can see that for the first monthly payment of $634.29, $222.29 goes towards reducing the principal amount, while $412 goes towards paying off the interest. Question 4 A couple has been granted a mortgage loan at an annual interest rate of 7 percent for 25 years. The home has as selling price of $98,750. They need a 25 percent down payment on their new home. What is the monthly payment? How much of the first monthly payment goes toward reducing the principal? Answer To answer this question, we need to first understand what a mortgage loan is and how it works. A mortgage loan is a type of loan used to finance the purchase of a home or property. It is secured by the property itself, which means that if the borrower fails to make the payments, the lender can take possession of the property. In this scenario, the couple has been granted a mortgage loan at an annual interest rate of 7 percent for 25 years. This means that every year, the couple will have to pay 7 percent of the loan amount as interest, and the loan will be paid off in 25 years. This also means that the total amount they will have to pay back will be the initial loan amount plus the interest accumulated over the years. Now, let's look at the numbers mentioned in the question. The selling price of the home is $98,750. This means that the couple will have to take a loan of $98,750 to purchase the home. However, the couple will also need to make a 25 percent down payment on their new home, which is $24,687.50. This means they will have to pay this amount upfront and the remaining $74,062.50 will be the loan amount. To calculate the monthly payment, we will use the loan amount, interest rate, and loan duration. It is important to note that the interest rate is given in annual terms, and we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate by 12 (number of months in a year). So, the monthly interest rate will be (7/100)/12 = 0.00583. Now, we can use a mortgage calculator or a formula to find the monthly payment. For this answer, we will use the formula: Monthly Payment = P * [i(1 + i)^n] / [(1 + i)^n - 1] Where, P = loan amount i = monthly interest rate n = number of months Putting the values in the formula, we get: Monthly Payment = $74,062.50 * [0.00583(1 + 0.00583)^300] / [(1 + 0.00583)^300 - 1] = $521.14 Therefore, the monthly payment for this mortgage loan would be $521.14. Now, let's move on to the second part of the question. How much of the first monthly payment goes towards reducing the principal? To understand this, we need to know the components of a mortgage payment. A mortgage payment typically consists of four parts: principal, interest, taxes, and insurance (also known as PITI). However, for the sake of simplicity, we will only consider the principal and interest in this scenario. As we calculated earlier, the monthly payment is $521.14. Out of this, a certain portion goes towards paying off the interest, while the remaining amount goes towards reducing the principal. To find out the interest for the first month, we will multiply the monthly interest rate by the loan amount. So, the interest for the first month would be $430.93. This means that out of the first monthly payment of $521.14, $430.93 goes towards the interest, and the remaining $90.21 goes towards reducing the principal. To understand this concept further, we can create an amortization table for the first year of the mortgage loan. An amortization table shows the breakdown of each monthly payment, including how much of it goes towards the principal and how much towards the interest. It also shows how much of the principal is left after each payment. Month Payment Interest Principal Remaining Principal 1 $521.14 $430.93 $90.21 $73,972.29 2 $521.14 $430.31 $90.83 $73,881.46 3 $521.14 $429.69 $91.45 $73,789.01 4 $521.14 $429.06 $92.08 $73,695.92 5 $521.14 $428.44 $92.70 $73,602.22 6 $521.14 $427.81 $93.33 $73,507.89 7 $521.14 $427.18 $93.96 $73,412.92 8 $521.14 $426.55 $94.59 $73,317.32 9 Question 5 Assume zero taxes. The Black Gold Oil Company can lease equipment at $10,000 per year (first payment 1 year hence) for 10 years or purchased at a cost of $64,177. The company has a weighted average cost of capital of 15 percent. A bank has indicated that it would be willing to make the loan of $64,177 at a cost of 10 percent. Should the company buy or lease? There are no uncertainties. The equipment will be used for 10 years. There is zero salvage value. Answer The decision on whether to buy or lease equipment is crucial for any company, and even more so for the Black Gold Oil Company due to the significant costs involved. In order to make an informed decision, a thorough analysis of the financial implications of both options needs to be conducted. The first step in this analysis would be to establish the net present value (NPV) of both options. According to the given information, leasing the equipment would cost the company $10,000 per year for 10 years, with the first payment being made in one year. Using a 15% discount rate, the NPV can be calculated as follows: NPV (lease) = -$10,000 + ($10,000/0.15)[1- (1+0.15)^-10] = $49,952.55 On the other hand, if the company chooses to purchase the equipment, the cost would be $64,177. Using the same discount rate of 15%, the NPV can be calculated as: NPV (buy) = -$64,177 + ($0/0.15)[1- (1+0.15)^-10] = -$64,177 Based on the NPV calculations, it is evident that leasing the equipment would be a more financially feasible option for the Black Gold Oil Company. However, it is essential to consider other factors that may influence the decision. One crucial factor is the cost of capital, as it affects the discount rate used in the NPV calculations. According to the given information, the company's weighted average cost of capital (WACC) is 15%. However, if the bank is willing to provide a loan at a cost of 10%, it would be more cost-effective for the company to finance the purchase. In such a scenario, the NPV for buying the equipment would be calculated as: NPV (buy) = -$64,177 + ($0/0.10)[1- (1+0.10)^-10] = -$17,738.54 Comparing this NPV with the NPV for leasing, it is evident that purchasing the equipment would be a better option for the company. Furthermore, it is essential to consider the company's cash flows and the impact on its financials. Leasing the equipment would result in lower initial cash outflows, making it a more attractive option for companies with limited cash reserves. On the other hand, purchasing the equipment would result in higher initial cash outflows but lower recurring costs.