Question

In: Finance

ohn and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at...

ohn and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).

So far, John and Daphne have accumulated $12,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?

Question 10 options:

$3,758.85

$3,595.43

$4,085.71

$4,004.00

$4,698.57

Solutions

Expert Solution

Formula sheet

A B C D E F G H I J K L M N O P
2
3 Cost of college eduction in todays dollar 14500
4 Education cost inflation 0.035
5 Rate of return 0.09
6 Duration of College 4 Years
7 Assuming A is the savings during years 5, 6 and 7.
8 To meet the college cost, the NPV of the above Cash flows should be zero.
9 NPV of the Cash Flows can be calculated as follows:
10 Year (n) 0 1 2 3 4 5 6 7 8 9 10 11
11 Cash Flow 12000 5000 5000 5000 5000 A A A =-$D$3*(1+$D$4)^L10 =-$D$3*(1+$D$4)^M10 =-$D$3*(1+$D$4)^N10 =-$D$3*(1+$D$4)^O10
12 Required rate of return (i) =D5
13 Present Value Factor (P/F,i,n) =1/((1+$D$12)^D10) =1/((1+$D$12)^E10) =1/((1+$D$12)^F10) =1/((1+$D$12)^G10) =1/((1+$D$12)^H10) =1/((1+$D$12)^I10) =1/((1+$D$12)^J10) =1/((1+$D$12)^K10) =1/((1+$D$12)^L10) =1/((1+$D$12)^M10) =1/((1+$D$12)^N10) =1/((1+$D$12)^O10)
14 Present Values of Cash Flows =D11*D13 =E11*E13 =F11*F13 =G11*G13 =H11*H13 0.65A 0.60A 0.55A =L11*L13 =M11*M13 =N11*N13 =O11*O13
15 NPV =$12000+$4587+$4208+$3861+$3542 ++(0.65+0.60+0.55)A - $9582-$9099-$8640-$8204
16 =$28,199+(0.65+0.60+0.55)A-35525
17 =1.80A-$7327
18
19 Since NPV should be zero, therefore
20 0=1.80A-$7327
21
22 Solving the above equation,
23 A= =-(SUM(D14:H14)+SUM(L14:O14))/SUM(I13:K13) =-(SUM(D14:H14)+SUM(L14:O14))/SUM(I13:K13)
24
25 Hence amount to be saved during year 5, 6, and 7 is =D23
26 Thus the third option is correct.
27

Related Solutions

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at...
John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own....
Jim and Elsie are saving for their granddaughter Amy’s college education. Amy just turned 12 (at...
Jim and Elsie are saving for their granddaughter Amy’s college education. Amy just turned 12 (at t = 0), and she will be entering college 6 years from now (at t = 6). College tuition and expenses at Sam Houston State University are currently $15,000 a year, but they are expected to increase at a rate of 2% a year. Amy should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on...
Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just...
Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years¾if she takes longer or wants to go to graduate school, she will be...
You and your partner are saving for your son Sam's (who today turned 10) college expenses....
You and your partner are saving for your son Sam's (who today turned 10) college expenses. Sam will enter college eight years from today. Annual tuition and other expenses at UCLA are currently $14,500, but they increase at a rate of 3.5 percent every year. Sam, you hope, will graduate in four years. Naturally, you need to pay tuition (and other fees) at the beginning of each year (at t = 8, 9, 10, and 11). So far, you and...
Patrick and Lydia are a couple with their daughter Nina, who has just turned 2. They...
Patrick and Lydia are a couple with their daughter Nina, who has just turned 2. They live in Norfolk. Lydia has been working part-time after her maternity leave (20 hours per week) and could carry on doing so until Nina is in primary school. However, Lydia is reconsidering and is looking into going back to a full-time job now rather than in 3 years’ time. Patrick is a full-time librarian and works 40 hours per week. Nina currently attends a...
You want to start saving for your son's college education. You will need $150,000 in 10...
You want to start saving for your son's college education. You will need $150,000 in 10 years. You can earn 6% compounded annually. How much do you need to invest today to pay for the entire education?
2. You are currently saving for your child's college education. The current cost of college is...
2. You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have...
You are currently saving for your child's college education. The current cost of college is $10,000...
You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all...
A father is saving to put his daughter through college. She is 5 years old, will...
A father is saving to put his daughter through college. She is 5 years old, will enroll in 13 years, and should graduate 4 years after that. Assume all college costs are paid upfront at the beginning of the year annually. Currently, college costs $18,000 per year, but is expected to increase 3% per year. He currently has $10,000 saved and his account earns 8% annually. He plans on making 13 equal deposits starting one year from today. How large...
You are saving for the college education of your two children. They are two years apart...
You are saving for the college education of your two children. They are two years apart in age; one will begin college in 7 years, and another in 10 years. You estimate your first child’s college expenses to be $30,000 per year, paid at the beginning of each college year (first payment is at year 7 and so on). You estimate your second child’s college expenses to be $50,000 per year, paid at the beginning of each college year (first...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT