Management the financial resources of firm - Курс лекций

(1 r ) Example: You borrow $5 mln. at 10 % of interest on 5 years. Starting the second year the interest rate will increase on 2% every year. Calculate the future value of the sum. F=5 (1.1 1.12 1.14 1.16 1.18)=9.612 Discounting semi-annually, monthly and daily. Sometimes financial transactions take place on the basis that interest will be calculated more frequently than once a year. For instance, if a bank account paid 12 % nominal return per year, but credited 6% after half a year, in the second half of the year interest could be earned on the interest credited after the first six month. This will mean that the true annual rate of interest will be grater than 12 %. The greater the frequency with which interest is earned, the higher the future value of the deposit. Example: If you put $10 in a bank account earning 12 % per annum then your return after one year is: 10(1 0.12)=11.20. Di - the possible value for some variable. Pi - the probability of the value D occurring. Company A: Possible sales value (Di) Probability (Pi), % Dix Pi $ 600 5 30 $ 800 10 80 $ 1000 70 700 $ 1200 10 120 $ 1400 5 70 м(Db) = 1000 Company B: Possible sales value (Di) Probability (Pi), % Dix Pi $ 200 4 8 $ 400 7 28 $ 600 10 60 $ 800 18 144 $ 1000 22 220 $ 1200 18 216 $ 1400 10 140 $ 1600 7 112 $ 1800 4 72 м(Db) = 1000 We now know that the mean of Company A’s and Company B’s sales forecast distribution is $1000. We are ready to calculate the standard deviation of the distribution using the following formula: у = For Company A: у = v(600-1000)2Ч0.05 (800-1000)2Ч0.1 (1000-1000)2Ч0.7 (1200-1000)2Ч0.1 (1400-1000)2Ч0.05 = v24000 = 155 For Company B: у = v(200-1000)2Ч0.04 (400-1000)2Ч0.07 (600-1000)2Ч0.1 (800-1000)2Ч0.18 (1000-1000)2Ч0.22 (1200-1000)2Ч0.18 (1400-1000)2Ч0.1 (1600-1000)2Ч0.07 (1800-1000)2Ч0.04= v148000 = 385 As you see, Company B’s standard deviation of 385 is over twice that of Company A. This reflects the greater degree of risk in Company B’s sales forecast. The greater the standard deviation value, the greater the uncertainty as to what the actual value of the variable in question will be. The greater the value of the standard deviation, the greater the possible deviation from the mean. Whenever we want to compare the risk of investments that have different means, we use the coefficient of variation. We were safe in using the standard deviation to compare the riskiness of Company A’s possible future sales distribution with that of Company B because the mean of the two distributions was the same ($1000). If operating income is relatively constant, as in the grocery store example, then there is relatively little uncertainty associated with it. If operating income can take on many different values, as is the case with the gold mining firm, then there is a lot of uncertainty about it. We can measure he variability of company’s operating income by calculating the standard deviation of the operating income forecast. A small standard deviation indicates little variability, and therefore little uncertainty. A large standard deviation indicates a lot of variability, and great uncertainty. Some companies are large and others small. So to make comparisons among different firms, we must measure the risk by calculating the coefficient of variation of possible operating income values. The higher the coefficient of variation of possible operating income values, the greater the business risk of the firm. Tables below show the expected value, standard deviation, and coefficient of variation of operating income for Company А and Company В, assuming that the expenses of both companies vary directly with sales (that is, neither company has any fixed expenses).