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CFA 2018 q6 a

Mariana earned a pre-tax annual salary of ORP 250,000 last year. Her salary will increase each year at the expected inflation rate of 3% and is taxed at 25%. Mariana has a defined-benefit pension plan, and she is fully vested.   
 
Last year, the Hidalgos’ living expenses were ORP 280,000. These expenses will increase each year at the expected inflation rate of 3%. The Hidalgos will reevaluate their spending upon Mariana’s retirement.  
 
The Hidalgos’ taxable investment portfolio is valued at ORP 4,000,000. The portfolio includes ORP 1,000,000 in the equity shares that Juan received from the sale of his company. In the rest of the portfolio, the Hidalgos prefer short-term fixed income and cash investments rather than equities. They own a home with no mortgage, valued at ORP 1,250,000, which is excluded from the investment portfolio. Investment returns are taxed at 25%.   
 The Hidalgos’ funding goal is to maintain the after-tax real value of their portfolio after making a donation to support a research organization. The donation is not deductible for tax purposes. They want to determine the maximum amount they can donate immediately that will allow the remaining portfolio to continue to fund their net cash need next year. Their advisor expects the portfolio to have a real after-tax return of 2.75% per year. 
 A. Determine, given the Hidalgos’ funding goal for the next year, the maximum amount  (in ORP) that can be donated immediately. Show your calculations. 

Guideline answer:

Calculate next year’s net cash needs: 
 
Inflow: Ordinary income × (1 + inflation rate) × (1 – tax rate) = 250,000 × (1 + 3.0%) × (1 – 25%) = 193,125 Outflow: Living expenses × (1 + inflation rate) = 280,000 × (1 + 3.0%) = 288,400

Next year’s net cash needs: Outflow – Inflow:  288,400 – 193,125 = 95,275 
 
• Calculate the minimum size of the portfolio (min Portfolio) that can meet next year’s net cash needs using the expected real after-tax return (2.75%): 
 
min Portfolio × net expected return = next year’s net cash needs min Portfolio × 0.0275             

min Portfolio = 3,464,545                
• Calculate the maximum donation (max Donation) that can be made today based on the difference between the existing portfolio size and the minimum portfolio size that can meet next year’s net cash needs: 
 
max Donation = existing Portfolio – min Portfolio             max Donation = 4,000,000 – 3,464,545             max Donation = 535,455 
 

Why was the deficit for the current year not deducted from the investment portfolio value to compute the donation required? Shouldn’t it be (400000-95275)-3464545

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the deficit is the amount that the fund needs to earn

It's a long shot, gotta make it.

The answer explanation is terrible.

They are using the current year deficit, but calling it next year’s salary.

Last year’s end of year salary and expense used for last year is 250k and 280k. So this year’s end of year salary and expense is 257.5k and 288.4k. This year’s shortfall is 95,275.

They need to fund 95,275 at the end of this year to fund this year’s consumption.

95,275/.0275 = 3,464,545.45

I’m not 100% sure why you use 2.75% and not 5.75%. But my theory is that the portfolio actually earns 5.75%, but you are only pulling out 2.75% worth of the portfolio.