PROBLEM 1.2. A firm is borrowing today a sum of SEK 8000 000. The loan will be repaid in four yearly installments of equal amounts, calculated at the rate of interest of 5%. 1.2.1. Calculate the value of each payment - which we denote below by p. 1.2.2. Each one of the yearly payments on the loan can be viewed as the sum of an interest payment and a principal repayment. If we consider for example the first payment, then a sum equal to SEK 80000000.05 covers the interest accrued over the same year, whereas the residual sum of SEK s1=p80000000.05 covers the repayment of a part of the principal. A similar observation can be made relatively to the second payment, except that the interest payment will be SEK (8000000s1)0.05. The residual sum will again cover the repayment of a part of the principle, and the process will continue until the loan is fully repaid. What is the amount of the interest payment and the principal repayment for each one of the five payments due by the firm? 1.2.3. A government agency has announced that the interest payments on funds borrowed during the current year by a category of firms that includes our firm will be subsidised. The amount of the subsidies will be equal to 10% of the total yearly interest payment, until the loan is extinguished. What is the subsidised part of each one of the payments calculated in 1.2.2, and what is the present value of the subsidies for the firm? 1.2.4. Policy interventions such as the one in 1.2.3 entail the risk of manipulation - if the firm makes greater interest payments, it will receive a greater amount of subsidies! Show one way in which the firm could change the profile of the payments on the loan in such a way that (i) the present value of the payments received by the bank, calculated at the rate of 5%, would remain equal to 8000000 , and (ii) the firm could increase the present value of the subsidies received; do justify your answer by providing the necessary calculations. PROBLEM 1.2. A firm is borrowing today a sum of SEK 8000 000. The loan will be repaid in four yearly installments of equal amounts, calculated at the rate of interest of 5%. 1.2.1. Calculate the value of each payment - which we denote below by p. 1.2.2. Each one of the yearly payments on the loan can be viewed as the sum of an interest payment and a principal repayment. If we consider for example the first payment, then a sum equal to SEK 80000000.05 covers the interest accrued over the same year, whereas the residual sum of SEK s1=p80000000.05 covers the repayment of a part of the principal. A similar observation can be made relatively to the second payment, except that the interest payment will be SEK (8000000s1)0.05. The residual sum will again cover the repayment of a part of the principle, and the process will continue until the loan is fully repaid. What is the amount of the interest payment and the principal repayment for each one of the five payments due by the firm? 1.2.3. A government agency has announced that the interest payments on funds borrowed during the current year by a category of firms that includes our firm will be subsidised. The amount of the subsidies will be equal to 10% of the total yearly interest payment, until the loan is extinguished. What is the subsidised part of each one of the payments calculated in 1.2.2, and what is the present value of the subsidies for the firm? 1.2.4. Policy interventions such as the one in 1.2.3 entail the risk of manipulation - if the firm makes greater interest payments, it will receive a greater amount of subsidies! Show one way in which the firm could change the profile of the payments on the loan in such a way that (i) the present value of the payments received by the bank, calculated at the rate of 5%, would remain equal to 8000000 , and (ii) the firm could increase the present value of the subsidies received; do justify your answer by providing the necessary calculations
