ACCT224 Assignment 3
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ASSIGNMENT 3
ANSWER 1 Based on the information provided, we will analyse the costs and advantages connected with this choice to determine whether Honda Motor Company should offer a $2000 rebate on its minivan.
1. **Rebate Cost:** Honda would pay $2,000 per vehicle for the additional 15,000 vehicles sold (out of a
total of 55,000).
Total Rebate Cost: $2000 multiplied by 15000 is $30,000,000.
2. **Profit Margin:** Honda makes $6,000 each vehicle in profit.
Total Revenue Increased by $6,000 * 15,000 = $90,000,000
Benefits include: 1. **Increased Sales Revenue:** - Honda will make more money from sales after moving from 40,000 to 55,000 automobiles.
Additional Sales Revenue is equal to $28,000 (price with rebate) multiplied by 15 to equal $420,000,000**.Net Benefit: Net Benefit is calculated as follows: Additional Sales Revenue - Total Rebate
Cost
Net Benefit is equal to $420,000,000 minus $30,000,000, or $390,000,000.
This research shows that the $2000 rebate would result in a net gain of $390,000,000. As a result, from a
financial standpoint, it seems wise for Honda Motor Company to grant the refund because it results in a sizable net advantage.
ANSWER 3 a) We will compute the value of both alternatives, $5000 in cash and 100 shares of the company's stock, to help you decide which form of the bonus you should choose and how much it will be
worth.
First Choice: $5,000 in Cash
This option has a $5000 value, which is clear.
Choice 2: 100 shares of the business's stock
100 shares of the company's stock are valued as follows:
Shares x Current Stock Price equals Stock Value
Number of Shares x Current Stock Price equals Value of Stock.
We may determine the worth of 100 shares by using the current stock price of $63 per share:
Value of Stock = 100 Text Shares multiplied by $63text each share equals $6300
Given that the value of the stock in this instance is higher than the value of the cash bonus ($5000), receiving 100 shares of the company's stock is more valuable than receiving the cash bonus ($5000).
I'll select the 100 firm shares because their worth ($6300) exceeds that of the $5000 cash incentive.
b) You must evaluate the prospective future performance of the company's shares to determine the potential future stock price. Choosing the stock bonus could be more advantageous if you think the stock
price will rise significantly over the course of the holding period of one year.
Review the company's financial standing, future growth possibilities, business plans, and any planned events or announcements that might have an impact on the stock price. A promising future could make the stock option more alluring.
Risk Tolerance: Take your financial status and risk tolerance into account. The $5000 cash bonus might be
the safer option if you prefer a guaranteed cash sum and have a lower risk tolerance.
Assess the diversity of your assets as well as your total financial portfolio. The cash bonus may be a wise choice for diversification if you already have a sizable percentage of your portfolio invested in the business or the sector.
Market volatility: Take into account the current market circumstances and volatility. You can choose the cash incentive for stability and immediate liquidity if the market is very erratic or unclear.
ANSWER 4 a) Savings Account Arbitrage: Assume you have $10,000 to deposit. At Bank One (5.5% interest rate): After one year, you would have $ 10 , 000 × 1.055 = $ 10 , 550 $10,000×1.055=$10,550. At Bank Two (6% interest rate): After one year, you would have $ 10 , 000 × 1.06 = $ 10 , 600 $10,000×1.06=$10,600. You can deposit your money in Bank Two and earn a higher return of $600. Arbitrage Gain for Savings = $ 10 , 600 − $ 10 , 550 = $ 50 $10,600−$10,550=$50 Loan Arbitrage: Assume you borrow $10,000. At Bank One (5.5% interest rate): After one year, you would owe $ 10 , 000 × 1.055 = $ 10 , 550 $10,000×1.055=$10,550. At Bank Two (6% interest rate): After one year, you would owe $ 10
, 000 × 1.06 = $ 10 , 600 $10,000×1.06=$10,600. You can borrow from Bank One and repay at Bank Two, saving money on interest. Arbitrage Gain for Loans = $ 10 , 550 − $ 10 , 600 = − $ 50 $10,550−$10,600=−
$50
b) Increased Loan Demand: Bank One offers loans at a lower interest rate (5.5%) than Bank Two (6%). Bank One is likely to witness an increase in loan demand given that clients often want the lowest interest
rates feasible on loans. All other things being equal, borrowers will favour Bank One for loans due to the lower interest rate.
Increase in Deposits: Compared to Bank One (5.5%), Bank Two (6%) offers a greater interest rate on savings. In order to maximise their profits, savers typically aim for the highest interest rates on their investments. Therefore, Bank Two is expected to experience a spike in deposits when customers choose to do so in order to benefit from the higher interest rate on deposits there.
c) Bank One's interest rate is 5%.
Increase in Loan Interest Rates: Bank One may decide to raise its loan interest rates in response to the surge in demand for loans brought on by the loans' lower interest rates. In an effort to maximise revenue
and control the influx of borrowers, this is a usual response to strong demand.
Possible Increase in Savings Interest Rates: Bank One may think about raising its savings interest rates to entice savers to choose their bank in order to compete with Bank Two and draw in more deposits.
Bank 2's interest rate is 6%.
Possible Reduction in Loan Interest Rates: In order to compete with Bank One, Bank Two may think about slightly lowering its loan interest rates. More price-sensitive borrowers may be drawn in with lower loan interest rates, however they would still try to strike a balance to sustain profitability.
Maintaining or Modifying Savings Interest Rates: In order to keep clients and effectively compete with Bank One, Bank Two may decide to maintain or slightly modify its savings interest rates if it continues to draw a flood of deposits.
Overall, both banks will probably strike a careful balance when increasing interest rates to maximise their income, draw in clients, and keep themselves competitive in the market. Interest rate modifications
will ultimately be determined by a number of variables, including market conditions, the competitive environment, regulatory environment, financial performance, and the strategic objectives of each bank.
ANSWER 10 We may use the present value calculation to determine how much you can borrow now (present value) to have $1,000 in a year while taking a 6% annual interest rate into account:
The formula reads: "[textPresentValue = fractextFutureValue"[1 + text "Interest Rate")[text "Time"]
provided values
- Future Value of $1000 (FV).
- The interest rate (r) is 6%, or 0.06 (in decimal form).
- Duration (t): One year
Fill in the formula using these values:
[text Present Value = frac 1000 (one plus 0.06) one]
[text|Present Value|approximately frac 1000 1.06|approximately 943.40]
So, at a 6% annual interest rate, you can borrow about $943.40 today to get $1000 in a year.
ANSWER 11 To calculate how much you will save in interest this year due to the reduction in the interest rate on your $12,000 loan, we'll first calculate the interest using both the original interest rate of 9% and the reduced interest rate of 7.5%, then find the difference.
Given values:
- Original loan amount (\(P\)): $12,000
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- Original interest rate (\(r_{\text{original}}\)): 9% or 0.09 (as a decimal)
- Reduced interest rate (\(r_{\text{reduced}}\)): 7.5% or 0.075 (as a decimal)
Interest with the original interest rate:
\[ \text{Interest}_{\text{original}} = P \times r_{\text{original}} \]
Interest with the reduced interest rate: \[ \text{Interest}_{\text{reduced}} = P \times r_{\
text{reduced}} \]
Now, calculate the interest savings for this year:
\[ \text{Interest Savings} = \text{Interest}_{\text{original}} - \text{Interest}_{\text{reduced}} \]
Substitute the given values and calculate:
\[ \text{Interest}_{\text{original}} = 12,000 \times 0.09 = 1,080 \]
\[ \text{Interest}_{\text{reduced}} = 12,000 \times 0.075 = 900 \]
\[ \text{Interest Savings} = 1,080 - 900 = 180 \]
You will save $180 in interest this year due to the reduction in the interest rate from 9% to 7.5%.
ANSWER 19 To calculate the present value of the savings bond, which represents what you should pay today for the bond that will pay $100 in 10 years at a 2% interest rate, we'll use the present value formula:
\[ \text{Present Value} = \frac{\text{Future Value}}{(1 + \text{Interest Rate})^{\text{Time}}} \]
Given values:
- Future Value (\(FV\)): $100
- Interest Rate (\(r\)): 2% or 0.02 (as a decimal)
- Time (\(t\)): 10 years
Plug these values into the formula:
\[ \text{Present Value} = \frac{100}{(1 + 0.02)^{10}} \]
\[ \text{Present Value} \approx \frac{100}{(1.02)^{10}} \]
\[ \text{Present Value} \approx \frac{100}{1.219024} \approx 82.03 \]
So, you should pay approximately $82.03 today for the bond that will pay $100 in 10 years at a 2% interest rate.
ANSWER 21 To rank the alternatives based on their present value given a 10% interest rate per year, we'll
calculate the present value of each alternative using the present value formula:
\[ \text{Present Value} = \frac{\text{Future Value}}{(1 + \text{Interest Rate})^{\text{Time}}} \]
Given interest rate (\(r\)): 10% or 0.10 (as a decimal)
1. **$100 received in 1 year:** \[ \text{PV}_1 = \frac{100}{(1 + 0.10)^1} = \frac{100}{1.10} \approx 90.91 \]
2. **$200 received in 5 years:**
\[ \text{PV}_2 = \frac{200}{(1 + 0.10)^5} = \frac{200}{1.61051} \approx 124.03 \] 3. **$300 received in 10 years:**
\[ \text{PV}_3 = \frac{300}{(1 + 0.10)^{10}} = \frac{300}{2.59374} \approx 115.66 \]
Ranking from most valuable to least valuable based on present value:
1. $200 received in 5 years (PV = $124.03)
2. $300 received in 10 years (PV = $115.66)
3. $100 received in 1 year (PV = $90.91)
Thus, considering a 10% interest rate per year, the $200 received in 5 years is the most valuable, followed by $300 received in 10 years, and then $100 received in 1 year.
B) If the interest rate is 5% per year, we'll recalculate the present value for each alternative and rank them accordingly. We'll use the present value formula:
\[ \text{Present Value} = \frac{\text{Future Value}}{(1 + \text{Interest Rate})^{\text{Time}}} \]
Given interest rate (\(r\)): 5% or 0.05 (as a decimal)
1. **$100 received in 1 year:**
\[ \text{PV}_1 = \frac{100}{(1 + 0.05)^1} = \frac{100}{1.05} \approx 95.24 \]
2. **$200 received in 5 years:**
\[ \text{PV}_2 = \frac{200}{(1 + 0.05)^5} \approx \frac{200}{1.27628} \approx 156.42 \]
3. **$300 received in 10 years:**
\[ \text{PV}_3 = \frac{300}{(1 + 0.05)^{10}} \approx \frac{300}{1.62889} \approx 184.29 \]
Ranking from most valuable to least valuable based on present value with a 5% interest rate:
1. $300 received in 10 years (PV = $184.29)
2. $200 received in 5 years (PV = $156.42)
3. $100 received in 1 year (PV = $95.24)
Thus, considering a 5% interest rate per year, the $300 received in 10 years is the most valuable, followed by $200 received in 5 years, and then $100 received in 1 year.
C) If the interest rate is 20% per year, we'll recalculate the present value for each alternative and rank them accordingly using the present value formula:
\[ \text{Present Value} = \frac{\text{Future Value}}{(1 + \text{Interest Rate})^{\text{Time}}} \]
Given interest rate (\(r\)): 20% or 0.20 (as a decimal)
1. **$100 received in 1 year:**
\[ \text{PV}_1 = \frac{100}{(1 + 0.20)^1} = \frac{100}{1.20} \approx 83.33 \]
2. **$200 received in 5 years:**
\[ \text{PV}_2 = \frac{200}{(1 + 0.20)^5} \approx \frac{200}{2.48832} \approx 80.45 \]
3. **$300 received in 10 years:**
\[ \text{PV}_3 = \frac{300}{(1 + 0.20)^{10}} \approx \frac{300}{6.19174} \approx 48.51 \]
Ranking from most valuable to least valuable based on present value with a 20% interest rate:
1. $100 received in 1 year (PV = $83.33)
2. $200 received in 5 years (PV = $80.45)
3. $300 received in 10 years (PV = $48.51)
Thus, considering a 20% interest rate per year, the $100 received in 1 year is the most valuable, followed by $200 received in 5 years, and then $300 received in 10 years.
ANSWER 29 To determine which option is better, we'll calculate the present value of the second option and compare it to the first option using a discount rate of 8%. We'll then choose the option with the higher present value.
1. **First Option: $100,000 right now (and nothing thereafter)**
Present Value of First Option (\(PV_1\)):
\[ PV_1 = \frac{100,000}{(1 + 0.08)^0} = 100,000 \]
2. **Second Option: $94,000 right now and $10,000 three years from now (and nothing after that)**
To calculate the present value of the $10,000 three years from now, we'll use the present value formula:
\[ PV_2 = \frac{94,000}{(1 + 0.08)^0} + \frac{10,000}{(1 + 0.08)^3} \]
\[ PV_2 \approx 94,000 + \frac{10,000}{(1.08)^3} \]
\[ PV_2 \approx 94,000 + \frac{10,000}{1.259712} \]
\[ PV_2 \approx 94,000 + 7,932.84 \]
\[ PV_2 \approx 101,932.84 \]
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Now, we compare the present values:
- \( PV_1 = 100,000 \)
- \( PV_2 \approx 101,932.84 \)
Since \( PV_2 \) (the present value of the second option) is higher than \( PV_1 \) (the present value of the first option), you should choose the second option: $94,000 right now and $10,000 three years from now.
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