# Corporate Finance

**Topics:**Net present value, Rate of return, Time value of money

**Pages:**9 (2053 words)

**Published:**March 11, 2013

1. If the first deposit is at 36 years and the last expected deposit is at 65 years, then annual deposits will be made for 30 years. Expected annual withdrawals are $90,000 for 15 years from the retirement fund with a bank that offers compound interest of 8% annually. Calculation

Present value (PV) =?

Future value (FV) = (90,000*15) = $1,350,000

Periodic payment amount (PMT) =?

Interest rate per period (Rate) = 8% or 0.08

Number of payment periods (Nper) = 30

Using the Excel function “PV”, the following data is entered into the presented fields Rate = 8%

Nper = 30

PMT =?

Fv = 1,350,000

Type = blank

PMT = $9,416.15

$9,416.15 is the amount required for 30 annual deposits with an 8% compound interest to yield $90,000 for 15 years.

2. If a lump sum amount is deposited on my 35th birthday, then the principle will be compounded for 31 years. Calculation

Using the compound interest formula

A = P (1+r/n) nt

Where; A = final amount, P = principal, r = interest rate n = number of times the interest is compounded per year and t = number of years

P= A/ (1+r/n) ntP = 1,350,000/ (1+0.08/1)31

P =1,350,000/ (1.08)31

P =1,350,000/ 10.868

The amount required for a lump sum deposit is $124,217.89

3.If an additional $1,500 from my employer bonus plan is deposited annually to the retirement account and a $25,000 is added to the account after 19 years (on my 55th birthday), then; using the total annual contribution obtained in (1), The first deductions from my annual contribution will be $1,500 from the bonus plan 4,471.98 – 1,500 = 2,971.98

Distributing the $25,000 over the 30 year period, (25,000/30) = 833.33 2,971.98 – 833.33 = 2,138.65

To make $90,000 withdrawals for 15 years, I will need to make annual deposits of $2,138.65 QUESTION 2:

1.

a) Net Present Value

Using the MS-Excel function of NPV the rate of return (12%) is keyed into the “Rate” field and the returns per period are keyed into the corresponding “Value” field to obtain the present value. For example returns of year 1 will be keyed into the “Value 1” field, returns of year 6 in the “Value 6” field as shown in the tables below. The NPV is obtained by subtracting the initial investment from the sum of the present values.

Option 1:

|Year |Returns |Present value | |1 |50,000 |$44,642.86 | |2 |50,000 |$39,859.69 | |3 |50,000 |$35,589.01 | |4 |50,000 |$31,775.90 | |5 |50,000 |$28,371.34 | |6 |50,000 |$25,331.56 | |7 |50,000 |$22,617.46 | |8 |50,000 |$20,194.16 | |9 |50,000 |$18,030.50 | |10 |550,000 |$177,085.28 | |Sum Of Present Values |$443,497.77 |

NPV for option 1 is (443,497.77-500,000) = -$56,502.23

Option 2:

|Year |Returns |Present value | |1 |60,000 |$53,571.43 | |2 |60,000 |$47,831.63 | |3 |60,000 |$42,706.81 | |4 |60,000 |$38,131.08 | |5 |60,000 |$34,045.61 | |6 |60,000 |$30,397.87 | |7 |60,000 |$27,140.95 | |8 |60,000 |$24,232.99 | |9 |60,000 |$21,636.60 | |10 |810,000 |$260,798.32 | |Sum Of Present Values...

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