Fundamentals of Corporate Finance, Questions 8, 9 and 11 from Page 107
8. Calculating Interest Rates. In 2010 the average price per metre for owner-occupied flats in Copenhagen was about 23.000 Danish kroner. In 1995 the average price was around 6.000 Danish kroner. What was the annual increase in selling price?
t = 2010 – 1995 = 16
FV= PV * (1 + r)^t
23.000 = 6000 * (1 + r)^16
(1 + r)^16 = 23.000/6000 = 3,83
1 + r = 3.83^(1/16) = 1.087552
1.087552 – 1 = 0.087552 = 0,088 r = 8.8%
9. Calculating the Number of Periods. You’re trying to save to buy a new 170.000 Ferrari. You have 40.000 today that can be invested at your bank. The bank pays 5 per cent annual interest on its accounts. How long will it be before you have enough to buy the car.
PV = FV / (1 + r)^t
40.000 = 170.000 / (1 + 0.05)^t
1.05^t = 170.000 / 40.000
1.05^t = 4.25 t = 29,656 (29 years)
0.656 * 12 = 7,872 (8 months)
29 years and 8 months.
11. Calculating Present Values. You have just received notification that you have won the 1 million first prize in the Euro Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 12 per cent? t = 80
PV = FV / (1 + r)^t
PV = 1.000.000 /
t = 2010 – 1995 = 16
FV= PV * (1 + r)^t
23.000 = 6000 * (1 + r)^16
(1 + r)^16 = 23.000/6000 = 3,83
1 + r = 3.83^(1/16) = 1.087552
1.087552 – 1 = 0.087552 = 0,088 r = 8.8%
9. Calculating the Number of Periods. You’re trying to save to buy a new 170.000 Ferrari. You have 40.000 today that can be invested at your bank. The bank pays 5 per cent annual interest on its accounts. How long will it be before you have enough to buy the car.
PV = FV / (1 + r)^t
40.000 = 170.000 / (1 + 0.05)^t
1.05^t = 170.000 / 40.000
1.05^t = 4.25 t = 29,656 (29 years)
0.656 * 12 = 7,872 (8 months)
29 years and 8 months.
11. Calculating Present Values. You have just received notification that you have won the 1 million first prize in the Euro Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 12 per cent? t = 80
PV = FV / (1 + r)^t
PV = 1.000.000 /