Please Answer All $15!$

Net Present Value $($PV Uneven Payment Series$)$: See NPV Calculation Notes PowerPoint

$1)$ Calculate the NPV of a machine which is bought for $$15,000,$ sold at the end of year $5$ for $$7,500,$ and produces the following cash flows: Year $1$ $$1,000,$ Year $2$ $$900,$ Year $3$ $$850,$ Year $4$ $$600,$ Year $5$ $$500,$ assume the cost of capital is $11\%.$

$2)$ Calculate the NPV of a machine which is bought for $$6,000,$ sold at the end of year $5$ for $$2,000\mathrm{.}00,$ and produces the following cash flows: Year $1$ $$2,000,$ Year $2$ $$1,750,$ Year $3$ $$1,500,$ Year $4$ $$1,000,$ Year $5$ $$500,$ assume the cost of capital is $8\%.$

$3)$ Calculate the NPV of a machine which is bought for $$12,000,$ sold at the end of year $7$ for $$4,000\mathrm{.}00,$ and produces the following cash flows: Years $1-3$ $$2,000,$ Year $4$ $$1,750,$ Year $5$ $$1,500,$ Year $6$ $$1,000,$ Year $7$ $$500,$ assume the cost of capital is $8\%.$

Inflation Adjusted Return $($PV of inflation$-$adjusted annuity due $-$BEG$)$

Don$$t forget to use the inflation adjusted interest rate formula,

$4)$ Julie is ready to retire. She wants to receive the equivalent of $$40,000$ in today$$s dollars at the beginning of each year for the next $25$ years. She assumes inflation will average $3\%,$ and she can earn a $10\%$ after$-$tax return $($compounded annually$)$ on her investments. What lump sum does she need to invest today to attain her goal?

$5)$ Diane and Andy are ready to retire. They want to receive the equivalent of $$75,000$ in today$$s dollars at the beginning of each year for the next $30$ years. They assume inflation will average $3\mathrm{.}5\%$ over the long run, and they can earn a $9\%$ after$-$tax return $($compounded annually$)$ on their investments. What lump sum do they need to invest today to attain their goal?

Internal Rate of Return $($IRR$)$

$6)$ Jake borrowed $$18,000$ from his father to purchase a camper. Jake paid back $$25,000$ to his father at the end of $6$ years. What was the average annual compound rate of interest on Jake$$s loan from his father?

$7)$ Billy purchased a certificate of deposit $5$ years ago for $$1,000.$ If the certificate of deposit is due today in the amount of $$2,000,$ what is the average annual compound rate of return assuming monthly compounding, that Billy realized on his investment?

Client$-$Related

$8)$ Your clients, Jim and Barbara, are both age $48.$ They have a household income of $$127,500.$ She has $$290,000$ of investment$/$retirement assets saved, not including personal assets. He has $$385,000$ of investment$/$retirement assets saved. Collectively, they save $12\%$ of their current household annual income for retirement. Assume they can expect to earn $7\mathrm{.}2\%$ with an inflation rate of $2\mathrm{.}9\%$ from now until their death. Since they are the same age, they both want to retire at age $62,$ and want to plan for a $75\%$ WRR$.$

How much will their collective retirement assets be worth at their retirement?

a$.$ $$2,136,567$

b$.$ $$2,215,398$

c$.$ $$1,117,535$

d$.$ $$1,987,358$

$9)$ Given the same information as in Q$8,$ approximately how many years will Jim and Barbara$$s retirement funds last in retirement?

a$.22\mathrm{.}4$ Years

b$.25\mathrm{.}0$ Years

c$.21\mathrm{.}6$ Years

d$.20\mathrm{.}2$ Years

Mortgage

$10)$ Your clients recently purchased their first home for $$329,000$ on August $15,$ with the first payment due September $15.$ They made a downpayment of $20\%$ and financed the balance over $30$ years at an annual interest rate of $4\mathrm{.}49\%.$

a$.$ What is their monthly mortgage payment?

b$.$ How much interest will they end up paying over the life of the loan?

Client Case

You have met with your clients a few times and are now ready to do their retirement needs analysis $($RNA$).$ The couple, filing Married Filing Jointly $($MFJ$),$ are both $39$ years of age and expect to work another $23$ years. They both plan on living to age $93.$ He currently earns $$60,000$; her $$58,333.$ Returns are expected to be $8\mathrm{.}2\%$ and inflation $3\mathrm{.}1\%.$ You and the clients have determined that they will cut $$47,234$ of their current expenses out upon retirement, but that they will see an increase of $$21,200$ in other areas.

Given the information above, please calculate the following for your client:

$11)$ What is your client$$s Wage Replacement Ratio?

$12)$ How much will they need to have saved at retirement to retire based on their WRR$?$

$13)$ How much will they need to save each year from now until retirement to retirement comfortably?

$14)$ How much will they need to save each year from now until retirement if they currently have saved $$125,000$ jointly in their $401($k$)$s and ROTH IRAs?

$15)$ If they currently have $$400,000$ saved, what annual rate of return do they need to earn, if they save $$2,500$ per month from now until retirement?

Please Solve All $15$