Question

f you invest $100 at an interest rate of 15%, how much will you have at the end of eight years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

please do not round intermediate calculations Round your answer to 2 decimal places

An investment costs $1,548 and pays $138 in perpetuity. If the interest rate is 9%, what is the NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Net present value

$

  

Future value

$

The interest rate is 10%.

  

a.	What is the PV of an asset that pays $1 a year in perpetuity?

  

Present value

$

  

b.	The value of an asset that appreciates at 10% per annum approximately doubles in seven years. What is the approximate PV of an asset that pays $1 a year in perpetuity beginning in year 8? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

  

Present value

$

  

c.	What is the approximate PV of an asset that pays $1 a year for each of the next seven years? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

  

Present value

$

  

d.	A piece of land produces an income that grows by 5% per annum. If the first year’s income is $10,000, what is the value of the land?

  

Present value

$

Answer 1

If we invest $100 at 15%, value at end of eight years is 100*(1.15)^8= 100*3.0590= $305.90

Given investment is 1548 and pays 138 in perpetuity. As present value of perpetuity is calculated as payment/discount rate, NPV is -1548+138/9%= -1548+1533.33= -14.67

a).

Given $1 at perpetuity. Present value of perpetuity is calculated as Payment/discount rate. So, 1/10%= 10

So, present value= $10

b).

Given it pays $1 as perpetuity beginning in year 8.

So, value at the end of year 7= 1/10%= 10. Present value is obtained by discounting it by 7 years.

So, 10/(1+10%)^7= 10/1.948= 5.13

So, present value is $5.13

c).

present value of equal payments can be calcated using present value of annuity formula: A*(1-(1+r)^-n)/r= 1*(1-(1.1)^-7)/10%= (1-0.513)/10%= 4.87

So, present value is $4.87

d).

Given income in first year is 10000 and it grows at 5%

its present value can be calculated using the formula P1/(r-g), where P1 is payment next year, r is rate of return and g is growth rate. On substituting, we get 10000/(10%-5%)= 200000

So, present value is $200000