Question

(a) Someone offers you a security which pays $n at the end of the nth year until forever (i.e., it pays $1 at the end of the first year, $2 at the end of the second year, and so on). If the annually compounded interest rate is10% per year, what is the fair price of such security?

(b) (Rule of 69) People in the banks have a quick way of finding outhow long it takes to double your money. The trick is to divide 69 by the continuously compounded interest rate (in percentage). For example,if the continuously compounded interest rate is 10% per year, then you know it takes 69/10 = 6.9 years to double your money. Why 69? Can you figure out a similar rule to find out the number of years it takes to triple your money? [Note: “Continuous compounding” means that thecompounding limit is∞; that is, if one dollar invested at interest rater, continuously compounded, then one year later the balance becomes e^r= limm→∞(1 +r/m)m.]

(c) You just signed a 30-year lease agreement for a business property. The monthly rent for the first year is $1,000/month, with the first monthly rent due today. Starting from the second year on ward, the monthly rent will be increased by 10%/year (i.e., the monthly rent for the second year will be $1,100, the monthly rent for the third year will be $1,000(1.10)2= $1,210,1 and so on). Assuming the annually compounded interest rate is 15%/year, what is the present value of the 360 rental payments.

Answer 1

1c)

Annual rental =1000*12=12000

Disount rate 15%

Year Annual rental Present value@15% Present Value

1 12000 0.870 10440

2 13200 0.756 9979

3 14520 0.658 9547

4 15972 0.572 9132

5 17569 0.497 8732

6 19326 0.432 8349

7 21259 0.376 7993

8 23385 0.327 7647

9 25724 0.284 7306

10 28296 0.247 6989

11 31126 0.215 6692

12 34239 0.187 6403

13 37663 0.163 6139

14 41430 0.141 5842

15 45573   0.123 5605

16 50130 0.107 5364

17 55143 0.093 5128

18 60657 0.081 4913

19 66723 0.070 4671

20 73395 0.061 4477

21 80735 0.053 4279

22   88809 0.046 4085

23 97690 0.040 3908   

24 107459 0.035 3761

25 118205 0.030 3546

26 130025 0.026 3381

27    143028 0.023 3290

28 157331 0.020 3147

29 173064 0.017 2942

30   190370 0.015 2856

Total 176543

7 b) Rule 114 can be used to determine how long it will take an investment to triple For Example At 10% an investment will triple in about 11 years (114/10)

7 a)

Assume CF from security is $100

Discount rate= 10%

Formula= CF/Discount rate

=100/0.10

Fair value of security = $1000

  

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