Problem Set: Calculating Net Asset Value
Problem Set . Calculating Net Asset Value
Calculate the net asset value for the Boston Equity mutual fund given total assets of $225,000,000, total liabilities of $5,000,000, and total shares of 4,400.
Suppose Shaan invested $10,000 of his own money with a $90,000 mortgage at 8.5%, and after three years sold the property for $120,000. Determine his gross profit, net profit/loss, and rate of return on investment.
Calculate Shelly’s net worth considering total assets of $108,800 and unpaid bills totaling $16,300.
Barry and Mary have over $4 million accumulated over 45 years of marriage. Determine the amount they can gift to their children and grandchildren without gift tax and the total estate removed from their estate.
For Dave’s rental property bought for $200,000 with a sale price of $240,000 after one year, calculate his return on investment both with the full cash purchase and with only $20,000 invested (interest-free loan from his father).
Determine insurance payout amounts for wind damage, theft, and vandalism based on deductibles and damages.
Calculate the future value of savings if Beverly and Kyle Nelson combine insurance premiums, saving 10% annually over ten years at 6% interest.
Estimate per capita health care spending in 10 years assuming a 5% annual increase from an initial $8,000 per person in 2008.
Assess whether Sarah's out-of-pocket health costs with her current insurance plan would be less with a stop-loss policy that caps expenses at $3,000, based on total costs of $8,893 and a deductible of $750.
Calculate the insurance payout for a family member with $1,100 in expenses under a plan covering 80% after a $500 deductible.
Determine the recommended life insurance coverage for a family wage earner earning $40,000 annually using the easy method.
Using the Consumer Buying Matrix, evaluate brands A, B, and C for a home entertainment center with attributes weighted by importance: portability (0.1), sound projection (0.6), warranty (0.3). Include other factors Tammy might consider.
Calculate buying and leasing costs for a vehicle, given initial costs, payments, estimated end value or charges, and opportunity cost interest rate.
Calculate the future value of $180 paid annually for appliance service contracts over 10 years at a 5% interest rate.
Find the future value of a $3,800 savings from selling a house instead of using a real estate agent, invested at 7% for five years.
Determine how much more John Walters pays with credit payments ($60 down + $34/month for 24 months) than a cash price of $695.
Paper For Above instruction
Calculating Net Asset Value and Related Financial Metrics: An Analytical Overview
Financial analysis forms the backbone of sound investment decision-making and wealth management. This paper discusses various fundamental financial concepts, including net asset value (NAV), rate of return, net worth, gift and estate tax considerations, investment return calculations, insurance claims, and future value estimations. These concepts are essential for individuals and institutions to assess their financial health, optimize wealth transfer strategies, and evaluate investment opportunities effectively.
Net Asset Value (NAV) Calculation of the Boston Equity Mutual Fund
The net asset value (NAV) offers a snapshot of a mutual fund's per-share value, computed by subtracting total liabilities from total assets and dividing the result by the number of outstanding shares. Given the total assets of $225 million, liabilities of $5 million, and 4,400 shares, the calculation proceeds as follows:
Net Assets = Total Assets - Total Liabilities = $225,000,000 - $5,000,000 = $220,000,000
Per-Share NAV = Net Assets / Total Number of Shares = $220,000,000 / 4,400 ≈ $50,000
This indicates each share of the Boston Equity mutual fund is valued at approximately $50,000, serving as a basis for investor valuation and fund performance assessment.
Investment Return Analysis: Shaan’s Property Investment
Shan's initial investment comprised $10,000 cash with a $90,000 mortgage, totaling an initial property value of $100,000. After three years, he sold the property for $120,000. The gross profit is the difference between the sale price and the initial investment:
Gross Profit = $120,000 - $100,000 = $20,000
However, the net profit must account for mortgage interest payments. The total interest paid over three years at 8.5% on $90,000 is calculated as:
Total Interest = $90,000 x 8.5% x 3 ≈ $22,950
Therefore, net profit/loss = Sale Price - Original Price - Total Interest = $120,000 - $100,000 - $22,950 = -$2,950, indicating a net loss. The overall rate of return considers the initial cash invested ($10,000) against the net profit or loss, leading to a negative return, highlighting the impact of financing costs on investment profitability.
Shelly’s Net Worth Calculation
Shelly's net worth is determined by subtracting her current unpaid bills from her total assets:
Net Worth = Total Assets - Unpaid Bills = $108,800 - $16,300 = $92,500
This net worth reflects her overall financial position, accounting for liabilities, and guides her financial planning.
Gift and Estate Tax Strategies for Barry and Mary
As they have accumulated over $4 million, Barry and Mary can gift up to the annual exemption limit without incurring gift tax. In 2008, the gift tax exemption per recipient was $13,000. With three children and five grandchildren, the total amount they can gift to their children is:
Gifts to children = 3 x $13,000 = $39,000
To grandchildren, similarly, they can gift:
Gifts to grandchildren = 5 x $13,000 = $65,000
The total estate transfer, including gifts and deductions, reduces their estate's taxable value. The combined estate utility is to minimize estate taxes legally and transfer assets efficiently.
Return on Investment: Dave’s Property Sale
Investing $200,000 in a rental property that appreciates to $240,000 yields:
Return = (Sale Price - Purchase Price) / Purchase Price = ($240,000 - $200,000) / $200,000 = 20%
When only $20,000 of personal funds are invested, with the remaining borrowed interest-free, the return on personal investment is significantly magnified, calculated as:
Return = ($240,000 - $200,000) / $20,000 = 200%
This exemplifies leverage's power in real estate investments, boosting returns substantially when debt is interest-free.
Insurance Claims and Payouts
Insurance payouts depend on damages and deductibles:
- Wind damage of $835 with a $500 deductible: Insurance pays = $835 - $500 = $335
- Theft of stereo worth $1,300 with a $250 deductible: Insurance pays = $1,300 - $250 = $1,050
- Vandalism causing $425 damage with a $500 deductible: Since damage is less than deductible, insurance pays = $0
Financial Savings and Investment Growth
The Nelsons’ combined premiums of $650 + $575 = $1,225 annually could save 10%, equating to approximately $122.50 yearly. Over ten years at 6% annual interest, the future value of these savings can be computed using the future value of an annuity formula:
FV = P \times \frac{(1 + r)^n - 1}{r} = 122.50 \times \frac{(1 + 0.06)^{10} - 1}{0.06} ≈ $1,459.88
Per Capita Health Care Spending Projection
Starting from $8,000 in 2008, with a 5% annual increase over ten years:
Future Spending = $8,000 \times (1 + 0.05)^{10} ≈ $8,000 \times 1.629 = $13,032
Cost Comparison: Sarah’s Insurance Policies
Sarah’s costs under her current plan involve a deductible of $750 and 85% coverage above that. Her total medical expenses are $8,893, so her out-of-pocket expenses are:
Remaining expenses after deductible = $8,893 - $750 = $8,143
Her insurance pays 85% of this amount: 0.85 \times $8,143 ≈ $6,921.55
Her out-of-pocket cost = $8,143 - $6,921.55 ≈ $1,221.45
Alternatively, a policy with a $3,000 cap would limit her out-of-pocket expenses, paying the entire $8,893 minus the cap, but as the cap is less than her total costs, she would still pay less than her current out-of-pocket expenses.
Health Insurance Adjustment and Family Coverage
The Kelleher family’s plan covers 80% of expenses after a $500 deductible per person. For expenses of $1,100, total deductible applies, and the insurance payout is:
Expenses beyond deductible = $1,100 - $500 = $600
Insurance pays 80% of $600 = $480, while the family pays the remaining 20% plus the deductible: $120 + $500 = $620 total out-of-pocket.
Life Insurance Needs Estimation
The "easy method" multiplies gross annual income by a factor (commonly 5-10). For a family earning $40,000, recommending coverage of about $200,000 to $400,000 ensures adequate protection and income replacement.
Consumer Buying Matrix and Vehicle Cost Analysis
In evaluating a home entertainment system, weights assigned to portability (0.1), sound projection (0.6), and warranty (0.3) help rank options based on performance scores. Additional factors in purchase decisions include brand reputation, price, and after-sales service.
Vehicle purchase costs include a down payment ($1,500), a loan payment ($450/month over 48 months), an estimated end-of-loan value ($4,000), whereas leasing involves monthly payments ($450 over 36 months) and end-of-lease charges. Opportunity costs are calculated at a 4% interest rate, impacting the overall cost comparison.
Additional Financial Calculations
The future value of yearly $180 appliance service payments over ten years at 5% interest equals approximately $2,159, computed via the future value of an annuity formula. Selling a home for $3,800 less than the cost of employing an agent, invested at 7% over five years, accumulates to about $4,538, demonstrating the benefit of alternative savings strategies.
John Walters’ credit payments totaling $60 down plus $34 monthly for 24 months amount to $60 + ($34 \times 24) = $900. Compared to the cash price of $695, he pays an additional $205, illustrating the incremental cost of credit financing.
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