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**CFA Practice Question**

Intelligent Semiconductor is considering the development of a new data storage medium, which will allow tremendous increases in the efficiency of its customers' high-end server lines. The development of the new system will take place in the firm's existing facilities and the storage costs for the additional equipment are expected to be residual in nature. The following information applies to this project:

Initial cash outlay: ($30,000)

t1: $11,000

t2: $15,000

t3: $15,000

t4: $15,000

t5 $5,000

Discount rate: 7.75%

Rent expense for existing facilities: ($2,500)

Initial cash outlay: ($30,000)

t1: $11,000

t2: $15,000

t3: $15,000

t4: $15,000

t5 $5,000

Discount rate: 7.75%

Assuming no taxes or related charges, that the initial cash outlay does not include any sunk costs, and no salvage value after the fifth year, which of the following choices best represents the discounted payback period for this investment?

A. 2.57 years

B. 2.77 years

C. 3.87 years

**Explanation:**Remember that the rental expense of the firm's existing facilities is a sunk cost and should not be incorporated into the calculation. This is due to the fact that the rental expense is not incremental in nature and is unaffected by the acceptance of the project in question. In this example, the discounted payback period is found by discounting the cash inflows at an annual rate of 7.75%. After the first period, the remaining balance to be recovered is {($30,000) + [$11,000/1.0775]}=($19,791.18). After the second period, the remaining balance to be recovered is found by the following: {($19,791.18) + [$15,000/1.16101]}=($6,871.36). The third period has a discounted cash inflow of $11,990.56, which is greater than the ($6,871.36) debit to be recouped. By dividing the amount needed to recoup the investment ($6,871.36) by the cash inflow from period 3, $11,990.56, we find a time period of 0.57 years. This figure is added to the two prior periods', yielding a discounted payback period of 2.57 years.

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**User Contributed Comments**
20

User |
Comment |
---|---|

gugli |
Can this be done on the 12C calculator some how? |

eddeb |
I have BAII plus, and it doesn't do that.. Have to buy the pro one... |

danlan |
Rent expense is a sunk cost and not counted. |

julamo |
well I'll pass on this one... |

jerepast |
11/1.075 + 15/1.075^2 = 23.21 for 2 yrs vs 30k up front... (30-23.21)/(15/1.075^3)=.57 of 3rd |

steved333 |
You know it's going to be b/w 2 and 3 years because you get 41,000 by the end of year 3. Even if you don't discount it, you have $4k to recoup after the second year. So you know that it will be closer to 2 years than 3, so process of deduction leads to 2.57 since that's closer to 2 than 2.77. |

Mariecfa |
BA II Pro Do the NPV Calculation. Scroll arrow down till you get DPB. Hit Compute and you will get the answer. |

Jasmine89 |
BA II Plus do not have this function? |

merrick |
just solve for the PV of t1,t2,t3 and do the simple pay back. 10208.82, 12919.83, 11990.56 30k-10208.82-12919.83=6871.35/11990.56=.57 plus the 2=2.57 |

sagania |
steved333 method works quite ok, the BA II plus doesnt have the one proposed by Marie, any suggestions? |

takor |
Sagania, check again. The BAII Plus does the calculation as proposed by Mariecfa |

aravinda |
If I understand correctly, since the manufacturing is done in the "firm's existing facilities"..this would be a sunk cost and hence 2500 is not included in the calculation...But if the company is renting the facility from someone, then the 2500 should be included...any thoughts... |

Yohan3109 |
very simple: enter cash flow initial -30000$ (dont add 2500 cause its sunk cost no related to the project) enter co1=11000$, co2 = 15000 for 3 years, and last one 5000$. hit NPV enter interst 7,75% cpt NPV use the arrow and select DPB for discount payback. |

mekc |
become one with your calculator.... |

mpapwa22 |
For sure mekc.....u r right. these cals can do anything. |

Tanuja78 |
BA II Plus doesn't do the calculation as stated by Yohan3109, the arrow keys only toggle between int and NPV. |

shiva5555 |
haha mekc. |

thebkr7 |
EASY super explained way: use CF enter the first 3 years enter 7.75% as i compute NPV(5,119.202) which will get you how much you made ontop of paying off your first -30k make year 3 payment your FV with i = 7.75% n = the 3 years and compute pv = 11,990.56 FINALLY 5119.20/11990.56 -1 = 0.57 plus your two years = 2.57 |

Horv |
Only the BA II Plus PROFESSIONAL has DPP. BA II Plus does not. |

pigletin |
so proud i have a BAII PRO |