TB problem week1

Which assertion is true?

* Can use a formula or FC FVt = Ck × (1+r)(t-k) * "K" is time invested at that year Albert: - Use the Compound Interest or FV formula 11200x(1.0882)^10 FV = 26079.85 FC: N=10, I=8.82, PV=-11200, PMT=0, FV? FV= 26079.85 Brooke: 18900x(1.0924)^3 (10-7th invested) FV = 24,638 FC: N=3, I=9.24, -18900, PMT=0, FV? FV= 24,638.08 Cassius: 16300 x (1.0826)^6 (10-4th invested) FV= 26241.92 FC: N=6, I=8.26, -16300, PMT=0, FV? FV= 26241.92 Therefore: C > A > B Answer is B

7. Euro Gyro just bought 50 cases of pita bread from Supply House. Euro Gyro has been offered the 3 possible payment options described in the table. If the discount rate is 14.3%, which of the assertions is true?

*** Note, asking from the SUPPLIER perspective. Want to sell more to have HIGHER MONEY! Option A *** Receiving money for FV (not negative) 6300/(1.143)^1 PV= 55118.11 FC: N=1, I= 14.3%, PV=?, PMT=0, FV= -6300 PV= 5511.811 Option B *** Receiving money for FV (not negative) FC: N=3, I= 14.3%, PV=?, PMT=0, FV= -8100 PV= 5424.33 Option C *** Receiving money for FV (not negative) FC: N=5, I= 14.3%, PV=?, PMT=0, FV= -10,700 PV= 5485 Therefore: Option A has the most money! A. Supply House should prefer option A more than option B, and Supply House should prefer option A more than option C

8. Danielle owns two investments, A and B, that have a combined total value of $25,000. Investment A is expected to pay $24,800 in 4 years from today and has an expected return of 12.79 percent per year. Investment B is expected to pay X in 7 years (FV) from today and has an expected return of 8.22 percent per year. What is X, the cash flow expected from investment B in 7 years from today?

*** On exams!!! WWK: A + B = 25k Step 1: Investment A PV0 = PV = Ct / (1 + r)^t FC: N=4, I=12.79, PMT=0, PV=?, FV=-24800 PV= 15,324 Step 2: Investment B - Since both A + B = 25000 - Subtract 25000 -15324 PV = 9,676 Step 3: X in 7th year or SOLVE for FV N= 7, PV= -9676, FV= ?, I=8.82 FV for B= 16820.87

5. What is X if X equals the value of investment A plus the value of investment B? Investment A is expected to pay $26,000 in 5 years from today and has an expected return of 14.19 percent per year. Investment B is expected to pay $37,000 in 9 years from today and has an expected return of 8.72 percent per year.

*** Will be on this EXAM 1 and FINAL!!! Step 1: Value Investment A PV0 = PV = Ct / (1 + r)t ****When they SAY VALUE = PV Present Value NOT FV PVa= 26000 / (14.19)^5 PVa= 13391.615 FC: N= 5, PV = ?, I=14.19, PMT=0, FV= -26000 (future paid in 5th year) PV= 13392 Step 2: Investment B N= 9, I=8.72, PV=?, PMT=0, FV= -37000 (future paid in 9th year) PVb= 37000/(1.0872)^9 Pvb= 17434.79 Step 3: A + B investment 13392 + 17434.79 = 30827 X= 30827

9. Cowboy Frozen Custard is planning to sell its Dallas, Houston, and San Antonio stores in S years from today. The firm expects to sell its Dallas store for a cash flow of $A, its Houston store for a cash flow of $A, and its San Antonio store for a cash flow of $B. The cost of capital for the Dallas store is Y percent, the cost of capital for the San Antonio store is Y percent, the cost of capital for the Houston store is X percent, A > B > 0, Y > X > 0, and S > 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which of the stores is most valuable?

- Which store is most VALUABLE? Use PV formula - Can use chart! WWK: A > B ($) Y > X (%) All Sales (t) happen in S years! Step 1: PV Formula D = A (1+y)^S H = A/1+x^S SA = B/1+Y^S Step 2: Compare each other - Comparing D to SA because the same Y% - D = A (1+y)^S > SA = B/1+Y^S - Because A > B - D > SA HOWEVER, - Comparing D to H because the same $A (Cfs) - D = A 1+y^S < H = A/1+x^S - Because smaller DENOMINATORS shrink less of the top number. So higher CFs - H > D ANSWER: B. The Houston store is the most valuable of the 3 stores

6. Fairfax Cookie just bought 2 tons of chocolate chips from Chantilly Chocolate. Fairfax Cookie has been offered the 3 possible payment options described in the table. If the discount rate is 9.0%, which of the assertions is true?

Option A PV0 = PV = Ct / (1 + r)t -10000 Option B: -12000/(1.090)^2 PV= -10,100 FC: N=2, I=9%, PV=?, PMT=0, FV= -12000 PV= -10100 Option C: -14000/(1.09)^4 PV= -9918 N=4, I=9%, PV=?, PMT=0, FV=-14000 PV= -9198 ***Want to pay as LITTLE as possible. So Option C is best option B. Fairfax Cookie should prefer option A more than option B and Fairfax Cookie should prefer option C more than option A

3. For each of the 4 investments described in the table, the investor would pay $500 today to purchase the investment. Each investment would have the annual return noted in the table and each investment would make a single, lump sum payment to the investor in the number of years from today noted in the table. If RA > RB and TQ > TZ, then which assertion is true? All annual returns and numbers of years from today when the single, lump sum payment will be made are greater than zero. Note that all investments that will make a single, lump sum payment in T years from today will make that payment at the same time and that all investments with an annual return of R have the same annual return.

Step 1: Compare A and B A: - 500 x (1+RA)^t B: - 500 x (RB)^t Therefore: Investment A is > than B Step 2: Compare Q and Z Q: 500 (1+r)^TQ Z: 500 (1+r)^TZ Therefore: Investment Q will take LONGER to grow > TZ Solution? Answer A: A and Q make larger lumps of payment Note: - Takes longer with the same Annual Rate, you get more money if it takes longer! (common sense?)

15. Four years ago, Mack invested $6,100. In 1 year from today, he expects to have $9,100. If Mack expects to earn the same annual return after 1 year from today as the annual rate implied from the past and expected values given in the problem, then how much does Mack expect to have in 4 years from today?

WWK: - Time -4 = 6100 - Year 1 = 9100 (receive) FV - Time jump 5 (to find R) - Time Jump 3 (from Year 1 to year 4. For step 2) - Use the 9100 for expected values Step 1: Find R FC: N= 5, PV=-6100, I=?, FV=9100 R=8.32% Step 2: Find FV for Year 4 FC: N= 3, PV= -9100, I=8.32%, FV= ? FV= 11,568.267

16. Two years ago, Ronaldo had $152,000 in his account. In 5 years, he expects to have $396,000. If he has earned and expects to earn the same return each year from 2 years ago to 5 years from today, then how much does he expect to have in 1 year?

WWK: - Time at Year -2, FV=152k - In Year 5, FV= 396k - Time Jump 7 years - Year -2 to year 1 - Year 1 of FV = ? Step 1: Find the R FC: N= 7, PV=-152000, I=?, FV= 396000 I= 14.658 Step 2: Find FV for Year 1 N=3, I=14.65, PV=152k, FV=? for year 1 PV= 229121.424 *** All the solving is the same as previous. BUT!!!! The questions ask about TWO YEARS AGO. So use the PV for 2 years ago

2. Two years ago, Rafer invested $1,600. He has earned and will earn compound interest of 8.50 percent per year. If Lainie invests $1,700 in 1 year from today and earns simple interest, then how much simple interest per year must Lainie earn to have the same amount of money in 6 years from today as Rafer will have in 6 years from today? Answer as an annual rate.

WWK: - Year -2 = 1600 - Year 6 = ? - N = 8 Step 1: Rafer in year 6 - C0 x (1+r)^t - 1600 x (1+.085)^8 FC: N Year 6 = 3,072.96 Step 2: Find the annual rate for Lainie in year 6 PV = [ C0 + (C0 x 1+r x t) - the new C0 is Time 1! 3072.96 = 1700 + [1700 x r x 5 ] 1372.966 = 8500SI SI = .1615 --> 16.15%

17. Four years ago, Jack invested $5,900. In 1 year from today, he expects to have $10,200. If Jack expects to earn the same annual return after 1 year from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does he expect to have exactly $17,200?

WWK: - Year -4: PV=-5900 - Year 1: FV= 10200 - Year jump from Y-4 to Y1 = 5 - Find R - Then Find the N (years) to get 17200 with the Rate Step 1: Find R N=5, PV=-5900, I=?, FV= 10200 I = 11.57% Step 2: Find the N Years to get 17200 N = ?, PV=10200, I=11.57, FV= 17200 N = 4.77 years from C1 (which is Year 1 not TODAY or C0) *** To Find from Today Just add 1 to 4.77 = 5.77 from C0

Based on the information in the table, which one of the assertions is true?

WWK: - comparing A and B (question marks) - comparing C and D - Valuable? So use PV formula Step 1: A: PV = Ct / (1 + r)^t = 6800/(1.1617)^3 = 4278.54 FC: N=3, I=16.7, PV=?, FV=6800 PV = 4278.55 B: = 8100/(1.1340)^5 = 4319.36 looks like B has more PV > A C: 2300 = 3800/(1+r)^6 (2300)(1+r)^6 = 3800 1+r^6 = 3800/2300 r^6 = (3800/2300) -1 r = (3800/2300)^1/6 -1 r= .0872 0r 8.72% FC: N=6, I=, PV=-2300, FV=3800 I = 8.72 D: 2900 = 5600/(1+r)^8 2900(1+r)^8 = 5600 1 +r = (5600/2900)^1/8 r = 1.0857 -1 r = .0857 or 8.57% FC: N=8, I=, PV=-2900, FV=5600 I = 8.573 Therefore which one is RISKIER? - Note, Higher Risk = Higher Return - Therefore, C has a higher Return? D Answer: Answer: C. Investment B is more valuable than investment A and investment C is riskier than investment D

13. Felicity owns two investments, A and B, that have a combined total value of $28,000. Investment A is expected to pay $25,000 in 4 years from today and has an expected return of 12.74 percent per year. Investment B is expected to pay $21,400 in 6 years from today and has an expected return of R per year. What is R, the expected annual return for investment B?

WWK: A + B = 28000 Step 1: Find PV of A FC: N=4, PV=?, I=12.74, FV=-2500 PV= 15474.901 Step 2: Subtract A from the total of two. Find B PV 28000-15474.901 = 12525.099 Step 3: Find R for B FC: N=6, PV=-12525.099, I=?, FV=21400 I = 9.33%

14. Alicia owns two investments, A and B, that have a combined total value of $31,300. Investment A is expected to pay $24,800 in 4 years from today and has an expected return of 12.72 percent per year. Investment B is expected to pay $27,100 in T years from today and has an expected return of 8.19 percent per year. What is T, the number of years from today that investment B is expected to pay $27,100?

WWK: A+B = 31300 Step 1: Find PV for A FC: N=4, PV=?, I=12.72, FV= -24800 PV = 15362 Step 2: Subtract to find PV for B 31300 - 15362 = 15938 Step 3: Find T years for B FC: N=?, PV=15938, I=8.19, FV= -27100 PV = 15362 I= 6.74 (Punch it CORRECTLY!)

10. Florida Fashion is planning to sell its Miami, Tampa, and Orlando stores. The firm expects to sell each of the three stores for the same, positive cash flow of $A. The firm expects to sell its Tampa store in S years, its Orlando store in S years, and its Miami store in T years. The cost of capital for the Tampa store is Y percent, the cost of capital for the Miami store is Y percent, the cost of capital for the Orlando store is X percent, T > S > 0, and Y > X > 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which one of the following assertions is true?

WWK: M: $A, T Years, Y% T: $A, S years, Y% O: $A, S years, X% T > S Y > X Step 1: Compare O=A/1+x^S vs T=A/1+y^S *like the previous problem. Smaller DEN. is better O=A/1+x^S > T=A/1+y^S T=A/1+y^S vs M= A/1+Y^T T>S, since T is in DEN. it will REDUCE the amount more T=A/1+y^S > M= A/1+Y^T Therefore: O > T > M C. The Orlando store is the most valuable of the 3 stores

11. East Coast Athletics is planning to sell its Wilmington, Philadelphia, and Boston gyms. The firm expects to sell its Wilmington gym for a cash flow of $A, its Philadelphia gym for a cash flow of $A, and its Boston gym for a cash flow of $B. The firm expects to sell its Wilmington gym in T years, its Philadelphia gym in S years, and its Boston gym in S years. The cost of capital for all three gyms is Y, B > A > 0, T > S > 0, and Y > 0. The cash flows from the sales are the only cash flows associated with the various gyms. Based on the information in the preceding paragraph, which one of the following assertions is true?

WWK: W: $A, T years, Y. A/(1+Y)^T P: $A, S years, Y. A/(1+Y)^S B: $B, S years, Y. B/(1+Y)^S B > A > 0 T > S > 0 Y > 0 (cost capital) Step 1: Compare PV = Ct / (1 + r)^t P vs B A/(1+Y)^S vs B/(1+Y)^S * Therefore Boston is Greater. B > P W vs P A/(1+Y)^T vs A/(1+Y)^S * Note, since T is bigger, but in the Denominator. * Therefore Philadelphia is MORE VALUABLE than W. Answer: Since Philly > Wilm (previous) and Boston greater than Philly tho. Therefore BOSTON is the most valuable C. The Boston gym is the most valuable of the 3 gyms

1. Three years ago, Caroline invested $7,500. She has earned and will earn compound interest of 3.2 percent per year. One year from today, Mardy can make an investment and earn a simple interest of 13.2 percent per year. If Mardy wants to have as much in 5 years from today as Caroline will have in 5 years from today, then how much should Mardy invest in one year from today?

What we know: - Year -3 = 7500 - Year 5 = ? - N = 8? Step 1: Caroline has in 5 years - PV = C0 x (1+r)^8 Compound interest - 7500 x (1.032)^8 = $9649.37 FC: N= 8 (-3 to 5) I= 3.2 (compound PV= -7500 FV5 = 9649.37 Step 2: Mardy in 5 years - Uses SIMPLE INTEREST (can't use FC!) PV = C0 + (C0 × simple interest rate per period × t) 9649.37 = [ C0 + (C0 x .132 x 4) (note 4 years. Year 1 -5) 9649.37 = .528CO + 1CO 9649.37 = 1.528C0 C0 = 6315.03 The answer is E: Less than 6500 or greater than 9300