You are thinking about opening a food truck focused on Poke Bowls outside of Haas. There...

          

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You are thinking about opening a food truck focused on Poke Bowls outside of Haas. There is some existing competition, but it serves "Poke Bowls" in which the fish is cooked, so no one will go there once your food truck is open. You estimate that it will cost $75k to purchase the truck at time zero. You will also need to purchase $5k of ingredients (inventory), but can pay for the ingredients later (you will have $5k of accounts payable). During your first year of operation, you anticipate sales of $50k. Both raw ingredients and labor, which are the two elements of your costs, are expensive ($20k each). Additionally, you will need to invest $5k in truck maintenance to offset the effects of depreciation. You plan to run a cashless business, and will have no accounts receivable or cash. You will maintain a constant level of inventory and accounts payable throughout the year, and you will pay a tax rate of 20%. (a) (1 point) What is the time zero free cash flow? That is, how much cash to do you need to start your business? (b) Show how to calculate the EBIT, unlevered net income, and free cash flow for your business during its first year (time one)? Do not include the initial startup costs (i.e. the time zero free cash flow). Express these variables (EBIT, UNI, and FCF) in terms of the numbers listed in the problem. You do not need to calculate exact numbers. (c) (1 point) Let us assume that your business will last forever, and the free cash flow will grow (after the first year) at the annual rate of inflation, 7 = 2%. If I tell you that the annual IRR is 7.33% and the annual discount rate is 6%, can you decide whether or not to start the food truck without calculating the NPV? If so, what should you decide? (d) (2 points) Under the same assumptions as the previous question (c), show how you would calculate the net present value of starting the busines, using the first-year free cash flow FCF1. You do not need to calculate an actual number. (e) (1 points) You are considering financing the purchase of the truck by selling a 5-year maturity bond issued at par. The bond will have semi-annual payments, and you believe you will have to promise a 4% bond-equivalent yield. What coupon (C) will you have to pay on the bond every six months, per $100 of bond face value? (f) (1 points) To get this yield on your bonds, you will need to make sure that the sum of your bond payments in the first year is no more than 40% of your EBIT in the first year. Show how you would solve for the maximum amount of money you can borrow by issuing bonds. You do not need to calculate an actual number. (g) (2 points) Immediately after you issue your bonds and start your business, inflation spikes. We now expect the annual rate of inflation to be 4% instead of 2%. The federal reserve responds by raising nominal interest rates, so that the annual real interest rate remains unchanged. Show how to calculate what the new nominal discount rate (an annual rate) must be. You do not need to calculate an actual number. (h) (2 points) As a result of the higher inflation, you now expect your food truck business to grow at a rate of 4%. You also expect your first-year free cash flows to be higher by a factor of 1.02 but of course the annual discount rate is now higher as well (see (g)). Has your food truck gone up or down in NPV? Hint: answering this question requires algebra, but no calculations. (i) (1 points) You issued your bond at par right before the inflation increase and resulting interest rate hikes mentioned in the previous problem. Without doing any calculations, determine whether the bond will become a premium bond, a discount bond, or remain at par following the interest rate hikes. (j) (2 BONUS points) Under the assumptions of question (f) (the one with the credit card interest rate and the original timeline), which option should I prefer? Answer without doing any non-trivial calculations, and the following hint: a 2% discount on $3000 is the same as a 3% discount on $2000, and 104 <0.97. You are thinking about opening a food truck focused on Poke Bowls outside of Haas. There is some existing competition, but it serves "Poke Bowls" in which the fish is cooked, so no one will go there once your food truck is open. You estimate that it will cost $75k to purchase the truck at time zero. You will also need to purchase $5k of ingredients (inventory), but can pay for the ingredients later (you will have $5k of accounts payable). During your first year of operation, you anticipate sales of $50k. Both raw ingredients and labor, which are the two elements of your costs, are expensive ($20k each). Additionally, you will need to invest $5k in truck maintenance to offset the effects of depreciation. You plan to run a cashless business, and will have no accounts receivable or cash. You will maintain a constant level of inventory and accounts payable throughout the year, and you will pay a tax rate of 20%. (a) (1 point) What is the time zero free cash flow? That is, how much cash to do you need to start your business? (b) Show how to calculate the EBIT, unlevered net income, and free cash flow for your business during its first year (time one)? Do not include the initial startup costs (i.e. the time zero free cash flow). Express these variables (EBIT, UNI, and FCF) in terms of the numbers listed in the problem. You do not need to calculate exact numbers. (c) (1 point) Let us assume that your business will last forever, and the free cash flow will grow (after the first year) at the annual rate of inflation, 7 = 2%. If I tell you that the annual IRR is 7.33% and the annual discount rate is 6%, can you decide whether or not to start the food truck without calculating the NPV? If so, what should you decide? (d) (2 points) Under the same assumptions as the previous question (c), show how you would calculate the net present value of starting the busines, using the first-year free cash flow FCF1. You do not need to calculate an actual number. (e) (1 points) You are considering financing the purchase of the truck by selling a 5-year maturity bond issued at par. The bond will have semi-annual payments, and you believe you will have to promise a 4% bond-equivalent yield. What coupon (C) will you have to pay on the bond every six months, per $100 of bond face value? (f) (1 points) To get this yield on your bonds, you will need to make sure that the sum of your bond payments in the first year is no more than 40% of your EBIT in the first year. Show how you would solve for the maximum amount of money you can borrow by issuing bonds. You do not need to calculate an actual number. (g) (2 points) Immediately after you issue your bonds and start your business, inflation spikes. We now expect the annual rate of inflation to be 4% instead of 2%. The federal reserve responds by raising nominal interest rates, so that the annual real interest rate remains unchanged. Show how to calculate what the new nominal discount rate (an annual rate) must be. You do not need to calculate an actual number. (h) (2 points) As a result of the higher inflation, you now expect your food truck business to grow at a rate of 4%. You also expect your first-year free cash flows to be higher by a factor of 1.02 but of course the annual discount rate is now higher as well (see (g)). Has your food truck gone up or down in NPV? Hint: answering this question requires algebra, but no calculations. (i) (1 points) You issued your bond at par right before the inflation increase and resulting interest rate hikes mentioned in the previous problem. Without doing any calculations, determine whether the bond will become a premium bond, a discount bond, or remain at par following the interest rate hikes. (j) (2 BONUS points) Under the assumptions of question (f) (the one with the credit card interest rate and the original timeline), which option should I prefer? Answer without doing any non-trivial calculations, and the following hint: a 2% discount on $3000 is the same as a 3% discount on $2000, and 104 <0.97.

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To calculate the time zero free cash flow we need to consider the i... View the full answer