1. A Retirement Problem

2. Model Setup  Financial Decision Saving/planning for retirement Saving/planning for retirement  Objective Have sufficient funds to support retirement Have sufficient funds to support retirement  Input Variables Spending during retirement ($30,000) Spending during retirement ($30,000) Expected return on investment (8%) Expected return on investment (8%) Amount of saving ($48,000) Amount of saving ($48,000)  Decision (bottom line) variable Account balance at the “end” Account balance at the “end”  Choice (discretionary) variable In this example, any of the input variables can be considered discretionary In this example, any of the input variables can be considered discretionary Use Amount of savings Use Amount of savings

3. Model Structure  Timing of deposits and withdrawals At the beginning of each year At the beginning of each year  Cash flow pattern of deposits and withdrawals Constant -> annuity dues Constant -> annuity dues  Number of years before retirement 5 years 5 years  Number of years in retirement 8 years 8 years

4. Formula Approach  Objective Amount of savings is sufficient to support retirement Amount of savings is sufficient to support retirement PV of deposits = PV of withdrawals PV of deposits = PV of withdrawals  PV of withdrawals Withdrawals starts at the end of year 5 (beginning of year 6) Withdrawals starts at the end of year 5 (beginning of year 6) A $30,000 annuity for 8 years A $30,000 annuity for 8 years The annuity formula (or Excel PV function) returns the lump sum value of the annuity at the end of year 4 The annuity formula (or Excel PV function) returns the lump sum value of the annuity at the end of year 4 PV4 = PMT5 * (1 – 1/(1+r)^8)/r PV4 = PMT5 * (1 – 1/(1+r)^8)/r PV0 = PV4 / (1+r)^4 PV0 = PV4 / (1+r)^4

5. Formula Approach (cont.)  PV of deposits PV0 of deposits = PMT1*(1–1/(1+r)^5)/r *(1+r) PV0 of deposits = PMT1*(1–1/(1+r)^5)/r *(1+r)  Solution Set PV0 of deposits = PV0 of withdrawals Set PV0 of deposits = PV0 of withdrawals Solve for PMT1 Solve for PMT1

6. Retirement Problem Worksheet

7. Extending the Retirement Model  The retirement age is “hard-coded” Cannot analyze the effects of delayed or early retirement Cannot analyze the effects of delayed or early retirement  Solution Make the retirement age an input variable Make the retirement age an input variable Use the IF() function to determine whether the cash flow will be a deposit or a withdrawal Use the IF() function to determine whether the cash flow will be a deposit or a withdrawal  Nested IF() functions