A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in the following collection of bonds to maximize the annual return.
Bond |
Annual Return |
Maturity |
Risk |
Tax Free |
A |
9.5% |
Long |
High |
Yes |
B |
8.0% |
Short |
Low |
Yes |
C |
9.0% |
Long |
Low |
No |
D |
9.0% |
Long |
High |
Yes |
E |
9.0% |
Short |
High |
No |
The officer wants to invest at least 40% of the money in short-term issues and no more than 20% in high-risk issues. At least 25% of the funds should go in tax-free investments, and at least 45% of the total annual return should be tax free.
Let the amount invested in Bond A be Xa, Bond B be Xb, Bond C be Xc, Bond D be Xd, Bond E be Xe
Based on the Annual returns rate given, total annual returns = 9.5%*Xa + 8%*Xb + 9%*Xc + 9%*Xd + 9%*Xe
We have to maximize this return, hence, we get Objective function as
Maximize Total returns R = 9.5%*Xa + 8%*Xb + 9%*Xc + 9%*Xd + 9%*Xe
Various constraints given can be written as follows:
Xa + Xb + Xc + Xd + Xe <= 150,000...........................Constraint for amount available for investment
Xb + Xc >= 40%*(Xa + Xb + Xc + Xd + Xe)................Constraint for minimum investment in short-term issues
Xa + Xd + Xe <= 20%*(Xa + Xb + Xc + Xd + Xe)........Constraint for maximum amount in high-risk issues
Xa + Xb + Xd >= 25%*(Xa + Xb + Xc + Xd + Xe).........Constraint for minimum investment in tax-free issues
9.5%*Xa + 8%*Xb + 9%*Xd >= 45%*(9.5%*Xa + 8%*Xb + 9%*Xc + 9%*Xd + 9%*Xe) .....................................................................................Constraint for minimum return to be tax-free
Xa, Xb, Xc, Xd, Xe >= 0...............................................Non-negativity constraint as investment cannot be negative
We solve the above problem in excel solver as shown below:
Above solution in form of formulas along with Excel Solver Extract is shown below for better understanding and reference:
Investment in Bond A = $30,000
Investment in Bond B = $38,964.5
Investment in Bond C = $81,035.5
Investment in Bond D = 0
Investment in Bond E = 0
Total Return = $13,260
-----------------------------------------------------------------------------------------------------------------------
In case of any doubt, please ask through the comment section before Upvote/downvote.
Kindly upvote the answer as it will be encouraging for me to keep answering further questions!!!
A trust officer at the Blacksburg National Bank needs to determine how to invest $150,000 in...
A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual return. Bond Yield Maturity Risk Task free A 9.50% LONG 0.996 YES B 8.00% SHORT 0.55 YES C 9.00% LONG 0.368 NO D 9.00% SHORT 0.775 NO E 9.00% LONG YES With the low risk score of bond E being uncertain, The officer wants the average risk score for his investments to be less than...
PLEASE ATTACH THE SPREAD SHEET 19. A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximine the annual retum. Annual Bulu Maturity Risk TaxFree 9.9% Long High Yes B 8.0% Short Low с 9.0% Long Low No D 9.0% Long High Yes No Short The officer wants to invest at least 50% of the money in short-term issues and no more than 50% in high-risk issues. At...
A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual return. Bond Yield Maturity Risk Task free A 9.50% LONG 0.996 YES B 8.00% SHORT 0.55 YES C 9.00% LONG 0.368 NO D 9.00% SHORT 0.775 NO E 9.00% LONG YES With the low risk score of bond E being uncertain, The officer wants the average risk score for his investments to be less than...
PLEASE ATTACH THE SPREAD SHEET 19. A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual retum Annual Bend Return Maturity A 95% Long High Yes 8.0% Short Low Long Low No D High Yes E 9.0% Short High No Long The officer wants to invest at least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least...
An investor has $20,000 to invest in a portfolio of three accounts. Account 1 offers a return of 2% and at a low risk. Account 2 offers a return of 4% and has a medium risk. Account 3 offers a return of 5% but at a relatively high risk. He decided to invest no more than $3000 into account 3 and at least twice as much in Account 1 into the investment of Account 2. a) Formulate this as a...
3. You just won a $100,000 lottery and plan to invest it among the following alternatives: Investment Global currency mutual fund (GF Energy mutual fund (EF Certificate of deposit (CD) Annual Return Rate 9% 7% 4% You want to invest this $100,000 in such a way to maximize your return from investment (in terms of dollars) one year from now, while meeting the following guidelines: . You must invest at least $20,000 in GF, and at most $30,000 in EF....
You just won a $100,000 lottery and plan to invest it among the following alternatives: You want to invest this $100,000 in such a way to maximize your return from investment (in terms of dollars) one year from now, while meeting the following guidelines: • You must invest at least $20,000 in GF, and at most $30,000 in EF. • The amount invested in CD should be at least as much as the amount invested in GF. • No more...
Problem 2-25 (Algorithmic) George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment a bond fund and 2) a stock fund. The pro ected returns over the life of the invest ents are 9% or the bond fund and 11%, forthe stock options: 1 nd. hate er portion of the inheritance he finally decides to commit...
The esteemed brokerage firm of Black, Scholes and Merton has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of Netflix, Inc. The client has a good deal of trust in the brokerage firm, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following...
3. JApplication of Linear Programming in Finance - Model Formulation (10 pts)] Jacksonville Trust Co. LTD invests in various types of securities. They have $12 million for immediate investment and wish to maximize the interest earned over the next year. Risk is not a uctor. Preferred investment alternatives include Bonds (B), Stocks (S), Gold (G), Land (L), BitCoin* (C), and famous Art Masterpieces (M). The expected return for Bonds is 5%, Stocks 12%, Gold 11%, Land 4%, BitCoin 2%, and...