Question

A local bank advertises the following deal: "Pay us $100 at the end of each year for 10 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever." a. Calculate the present value of your payments to the bank if the interest rate is 5.50%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the present value of a $100 perpetuity deferred for 10 years if the interest rate is 5.50%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

Part A. $754

Part B. $1064.42

Explanation:

Part A. The present value of payments can be calculated using the annuity formula which is as under:

Present Value = Cash flow * Annuity Factor

Here

Annual Payments = $100

Number of periods = 10

Interest rate = 5.5%

Annuity Factor = [1 - (1+i)^-n]  / i  = [1 - (1 + 5.5%)^-10] / 5.5% = 7.538  

Present Value = $100 * 7.538 = $754

Part B. The present value of $100 deferred perpetuity for 10 years can be calculated in two steps:

Step 1. Calculate the perpetuity at the year 10

Perpetuity = Cash flow / Discount Rate

Perpetuity = $100 / 5.5% = 1818.182

Step 2. Now discount this amount back to year zero.

Deferred Annuity = $1818.182 / (1.055)^10 = $1064.42

The value received is above the annual payments which means it is a good deal.

Answer 2

Answer:

1. $753.76

2. $1064.42

3.yes

Explanation:

Interest rate = 5.50% = 0.055

Period = 10years

Present value (PV) =

The present value of cash flow Is calculated by:

PV = 100/0.055*(1- (1/(1 + 0.055)^10))

PV = 100/0.055 × (1 - (1 / 1.055^10))

PV = 1818.18181818181818 × (1 - 0.58543057942760689)

PV = 753.762582858896555

2.) Present value of perpetuity:

100/(1 + 0.055)^11 × [1/(1 - (1/1 + 0.055))]

[100/1.055^11] × [1/(1 - 0.947867298]

55.4910501827115539 × 19.181817

= 1064.4192

3.) Yes, as it yield a greater value