Practice Problems

Practice Problems

IRR Example Problems 1.

Jacque bought a Picasso Painting 3 years ago for $20,000. Today, the  painting has been appraised at $52,000. What is Jacques IRR IRR (Internal Rate of Return)? Solution on HP 12C: f clx; g 8; 20,000 chs PV; 3 n; 52,000 FV; i = 37.51% is IRR 

2.

Benny bought 250 shares of Research in Motion stock 4 years ago for  $25,000. Today the shares are worth $35,250. What is Benny’s IRR? Solution on HP 12C: f clx; g 8; 25,000 chs PV; 4 n ; 35,250 FV; i = 8.97% is IRR 

3.

Sherry bought 200 shares of Peru Copper 2 years ago for $8,475. Sherry received quarterly dividends of $50. She just sold the stock for for $11,375. What is Sherry’s IRR? Solution on HP 12C: f clx; g 8; 8,475 chs PV; 50 PMT; 8 n ; 11,375 FV; i = 4.27 Enter 4 X = 17.07% is IRR 

4.

Lloyd Lloyd bought raw land 4 years ago for $100,000. His expenses related to the land were $8,000 the first year, $8,200 the second year, $7,800 the third year  and $7,900 the fourth year. Lloyd sold the land at the end of the fourth fourth year  for $175,000. What was Lloyd’s Lloyd’s IRR? Solution on HP 12C: f clx; g 8; 100,000 chs g CFo, 8,000 chs g CFj; 8,200 chs g CFj; 7,800 chs g CFj; 167,100 16 7,100 g CFj; f IRR = 8.53%

5.

Frank bought a corporate bond 4 years ago for $1,200. He received semiannual interest of $40. The bond matured today for its face amount of $1,000. What is Frank’s IRR? Solution on HP 12C: f clx; g 8; 1,200 chs PV; 40 PMT; 8 n ; $1,000 FV, i = 1.35%

PV Example Problems 6.

Calculate the present value of $10,000 to be received in exactly 10 years, assuming an annual interest rate of 9 %. Solution on HP 12C: f clx ; g 8 ; 10,000 FV ; 9 i ; 10 n ; PV = 4,224.11

7.

Calculate the Present Value of an ordinary annuity of $5,000 received annually for 10 years, assuming a discount rate of 9 %. Solution on HP 12C: f clx ; g 8 ; 5,000 chs PMT ; 9 i ; 10 n ; PV = 32,088.29

8.

Susan expects to receive $50,000 in 2 years. Her opportunity cost is 10 % compounded monthly. What is the sum worth to Susan today? Solution on HP 12C: f clx ; g 8 ; 50,000 FV ; 2 g n ; 10 g i ; PV = 40,970.47

9.

Elaine wants to have $500,000 in today’s dollars at his retirement 22 years from now. She already has accumulated a large investment portfolio and wants to know how much of it she should earmark for this goal. She believes she can earn 9% after tax and that inflation will average 3% over the period. How much must Elaine set aside to accomplish her goal? Solution on HP 12C: f clx; g 8 ; 500,000 FV, 22 n ; 1.09 ENTER 1.03 / 1 –  100 X i ; PV = 143,881.84

10.

Ethel wants to withdraw $3,000 at the beginning of each year for the next 5 years. She expects to earn 8 % compounded annually on her investment. What lump sum should Ethel deposit today? Solution on HP 12C: f clx ; g 7 ; 3,000 chs PMT ; 8 i ; 5 n ; PV = 12,936.38

PMT Example Problems 11.

Estelle wants to have $25,000 in today’s dollars for a cruise to Alaska when she retires 11 years from now. She assumes she can earn 6% after-tax and that inflation will be 2.5%. What does she need to save at the beginning of  each month to reach her goal? Solution on HP 12C: f clx; g7 ; 25,000 FV; 44 n; 1.06 ENTER 1.025 /1 – 100 x i; PMT =

12.

Raymond wants to buy a new yacht in 6 years. He believes it will cost $275,000 in today’s dollars. He thinks he can earn 10% after-tax and that the yacht prices will inflate at 4%. What must Raymond save at the end of this year to reach his goal if his plan is to save annually? Solution on HP 12C: f clx; g 8; 275,000 FV ; 6 n ; 1.10 ENTER /1 – 100 x I ; PMT = 39,654.50 but you must multiply that by the inflation rate of 4% since the question asks how much must he save at the end of the first year. So, PMT = 39,654.50 ENTER 1.04 x = 41,240.68

13.

Monk borrowed $240,000 at 8 % for 15 years. What would his first payment  be if it is due 30 days after the loan was made on January 30, 2007? Solution on HP 12C: f clx ; g 8 ; 240,000 PV ; 15 g n ; 8 g i ; PMT = 2,293.56

14.

Mona purchased a car for $25,000. She is financing the auto at a 10 % annual interest rate, compounded monthly for 4 years. What payment is required at the end of each month to finance Mona’s car? Solution on HP 12C: f clx ; g 8 ; 25,000 chs PV ; 10 g i ; 4 g n ; PMT = 634.06

15.

Josh purchased a house for $215,000 with a down payment of 20 %. If he finances the balance at 10 percent over 30 years, how much will his monthly  payment be? Solution on HP 12C: First, he paid down .20 of 215,000 so he is borrowing .80 of 215,000 = 172,000. So, f clx ; g 8 ; 172,000 PV ; 10 g i ; 30 g n ; PMT = 1,509.42

FV Example Problems 16.

What is the FV of $10,000 invested for 10 years, assuming an annual interest rate of 8%? Solution on HP 12C: f clx; g 8 ; 10,000 PV; 10 n ; 8 i ; FV = 21,589.25

17.

What is the FV of an Ordinary annuity of $5,000 received for 10 years, assuming an earnings rate of 9%? Solution on HP 12C: f clx; g 8 ; 5,000 PMT; 10 n ; 9 i ; FV = 75,964.65

18.

Marty invested $5,000 in an interest-bearing promissory note earning 8 % annual rate of interest compounded monthly. How much will the note be worth at the end of 5 years, assuming all interest is reinvested at the 8 % rate? Solution on HP 12C: f clx ; g 8 ; 5,000 chs PV; 60 n ; 8 g i ; FV = 7,449.23

19.

Bob has been dollar cost averaging in a mutual fund by investing $1,000 at the  beginning of every quarter for the past 5 years. He has been earning an average annual compound return of 11 % compounded quarterly on this investment. How much is the fund worth today? Solution on HP 12C: f clx ; g 7 ; 1,000 chs PMT ; 20 n ; 11 ENTER 4 / i ; FV = 26,917.83

20.

If Carlos invested $12,000 dollars for 10 years and he was getting an annual interest rate of 9.25 %, how much would his investment be worth at the end of  the 10 years? Solution on HP 12C: f clx ; g 8 ; 12,000 chs PV ; 10 n ; 9.25 i ; FV = 29,066.69